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Slope intercept form given two points calculator

Enter any Number into this free calculator $ \text{Slope } = \frac{ y_2 - y_1 } { x_2 - x_1 } } How it works: Just type the numbers into the box below and the calculator will automatically calculate the line equation in the form of standard tapping, point slope, and slope. How to enter a number: Enter any integer, decimal, or fraction. Fractions must be inserted with

forward slashes such as '3/4' for the $$ \frac{3}{4} $$ fractions. Linear Equation Worksheets All Math Calculators :: Analytical Geometry :: Two point shapes This online calculator can find and plot straight line equations that pass through two points. The calculator will generate a step-by-step explanation of how to get the results. example Specify a line

equation that passes the points $(-2, 5)$ and $(4, -2)$. Find the slope - a straight line shape that passes the points $\left( \frac{7}{2}, 4 \right)$ and $\left(\frac{1}{2}, 1 \right)$. If the dots $\left( 3, -5 \right)$ and $\left(-5, -1\right)$ are lying in a straight line, specify the shape of the slope intersection line. To find a line equation that passes through the dots

$A(x_A, y_A)$ and $B(x_B, y_B)$ ($x_A e x_B $), we use the formula: $$ {\color{blue}{ y - y_A = \frac{y_B - y_A}{x_B-x_A}(x-x_A) }} $$ Example: Find the line equation specified by $A(-2, 4)$ and $B(3, -2)$. Solution: In this example we have: $ x_A = -2,~~ y_A = 4,~~ x_B = 3,~~ y_B = -2$. So we have: $$ \begin{aligned} y - y_A & = \frac{y_B - y_A}

{x_B-x_A}(x-x_A) \\ y - 4 & = \frac{-2 - 4}{3 - (-2)}(x - (-2)) \\ y - 4 & = \frac{-6}{5}(x + 2) \end{aligned} $$ Times both sides with $5$ to get rid of fractions. $$ \begin{aligned} (y - 4)\cdot {\color{red}{ 5 }} & = \frac{-6}{5}\cdot {\color{red}{ 5 }}(x + 2)\\5y - 20 & = -6(x + 2)\\ 5y - 20 & = -6x - 12 \\ 5y & = -6x - 12 + 20 \\ 5y & = -56x +

8 \\ {\color{blue}{ y }} & {\color{blue}{ = -\frac{6}{5}x - \frac{8}{5} }} \end{aligned} $$ In special cases (when $x _A = x_B$ line equation is: $$ {\color{blue}{ x = x_A }} $$ Example 2: Find the line equation specified by $A(2, 4)$ and $B(2, -1)$. Solution: In this example we have: $ x_A = 2,~~ y_A = 4,$ $ x_B = 2,~~ y_B = -1$. Because $x_A = x_B$, the line

equation is: $$ {\color{blue}{ x = 2 }} $$ you can see from the image on the right that in the special case of the line is parallel to the y-axis. Note: use the calculator above to check the results. Search Quick Calculator 207 959 871 resolved problems There are several different ways to find line equations of 2 points. The first half of this page will focus on writing

equations in the form of slope tapping as example 1 below. However, if you are comfortable using the slant shape of the line point, then skip to the second part of this page because writing an equation of 2 points is easier with the shape of the point slope . Equation of 2 points using the Bevel Intersection Form Find the line equation through a point (3.7) and

(5.11) Step 1 Calculate the bevel of 2 2 Step 2 Step 3 Replace one of the dots into the equation. You can use Either (3,7) or (5.11) Solve Step 4 for b, which is the y-intercept of the line Step 5 Replacement b, -1, into the equation from step 2 Use our Calculator You can use the calculator below to find the line equation of the two dots. Just type the numbers

into the box below and the calculator (which has its own page here) will automatically calculate the equation of the line in the form of slope points and slope intersections Answer: $ $ ( Try this 'equation of 2 points' calculator on its own page here . ) Remove Alternating Point Practice Problems Find line equations through the following 2 points: (4.5) and (8.7)

Find line equations through the following points: (-6.7) and (-9.8) Step 1 Step 2 Replace slope to 'm' in the slope intercept equation Step 3 Replace one of the points into the equation. You can use Either (-6,7) or (-9.8) Step 4 Solve for b, which is the y-intercept of the Step 5 Substitute b line, 5, into the equation from step 2 $$ y = \frac{1}{3}x +\red{b} \\ y =

\frac{1}{3}x +\red{5} $$ Find line equations up to 2 points below: (-3.6) and (15,-6) Step 1 Step 2 Replace the slope for 'm' in the slope equation Step 3 of the equation. You can use (-3,6) or (15,-6) Step 4 Step 5 Replacement b, -1, into the equation from step 2 Of Example 2 Equation of 2 points using the Point Bevel Form As described at the top, the point

slope shape is an easier way to go. Instead of 5 steps, you can find line equations in 3 steps, 2 of which are very easy and require no more than replacement! In fact, the only calculation, which you will make is for the slope. The main advantage, in this case, is that you don't have to solve for the 'b' as you do by intercepting the slope from. Find equations of

lines through points (3,7) and (5.11) Step 1 Calculate the slope of 2 points Step 2 Replace the slope for 'm' in the point equation y - y1 = m(x -x1) y - y1 = 2(x -x1) Step 3 Replace one of the points as x1, y1 in the equation. You can use (3.7) or (5.11) use (3.7): y - 7 = 2(x- 3) using (5.11): y - 11 =2(x - 5) Exercise Problems Find a line equation through the

following 2 points: (4,5) and (8,7) Step 1 Calculate the slope of the 2-point Step 3 Replace one point into the equation. You can use (4.5) or (8.7) use (4.5): y - 5 = 1/2(x - 4) using (5.11) : y - 11 = 1/2(x - 5) If the line passes the following 2 points, what is the equation of the line? (-6,7) and (-9,8) Step 1 Calculate the slope of 2 points Step 3 Replace one of

the points into an equation. You can use (-6,7) or (-9.8) use (-6.7): y - 7 = (x + 6) using (-9, 8): y - 8 = (x +9) Find the equation of the line The following 2 points: (-3,6) and (15,-6) Step 1 Calculate the slope of 2 points Step 3 Replace one point into the equation -3.6) and (15,-6) use (-3, 6) : y - 6 = (x + 3) 3) (15, -6): y + 6 = (x - 15 ) If you read the entire page

and look at both methods (form of tapping the slope and slope of the point, You can see that it's substantially faster to find a line equation through 2 points by way of a point bevel The line bevel intersection shape is:y=mx+by = \textcolor{#F18F01}{\boldsymbol{m}}x + \textcolor{#A14DA0}{\boldsymbol{b}}y=mx+bThe m\textcolor{#F18F01}{\boldsymbol{m}}m

stands for bevel line and b\textcolor{#A14DA0}{\boldsymbol{b}}b stands for y-intercept of lines. Normally, we'll be given some information, and we'll have to find m\textcolor{#F18F01}{\boldsymbol{m}}m and b\textcolor{#A14DA0}{\boldsymbol{b}}b to connect it and get a line equation. The question may give you two points or one point and a slope. We have

steps for each below, or you can scroll down to our fancy step by step calculator. Our steps will differ based on the information we have, so which guide do we want? Select OptionTwo PointsOne Point + SlopeSo, remember, our equation is:y=mx+by = \textcolor{#F18F01}{\boldsymbol{m}}x + \textcolor{#A14DA0}{\boldsymbol{b}}y=mx+bm \textcolor{#F18F01}

{\boldsymbol{m}}m stands for bevel and b\textcolor{#A14DA0}{\boldsymbol{b}}b stands for y-intercept of the line. Steps to write this equation if we have two points below. First, let's call our points Point 1 with coordinates (x1,y1)\boldsymbol{\textcolor{#32936F}{(x_1,y_1)}}(x1 ,y1) and Point 2 with coordinates (x2,y2)\boldsymbol{\textcolor{#2274A5}{(x_2,y_2)}}

(x2 ,y2). Now, we're going to find a slope. Split changes in yyy with changes in xxx:m=slope=y1-y2x1-x2m = \text{slope} = \boldsymbol{\frac{\textcolor{#32936F}{y_1} - \textcolor{#2274A5}{y_2}}}{\textcolor{#32936F}{x_1} - \textcolor{#2274A5}{x_2}m=slope=x1 -x2 y1 -y2 Note the color encoding - make sure that the first xxx and yyy values in the subtraction

are from the same point. Now, let's pretend that the value we get for m\textcolor{#F18F01}{\boldsymbol{m}}m is 2\textcolor{#F18F01}{\boldsymbol{2}}2. We can reconnect it to our equation, so now we have =2x+by = \textcolor{#F18F01}{\boldsymbol{2}}x + \textcolor{#A14DA0}{\boldsymbol{b}}y=2x+b To get b\textcolor{#A14DA0}{\boldsymbol{b}}b, we just

plug in one of our points -y1=2(x1)+b\boldsymbol{\textcolor{#32936F}{y_1}} = 2(\boldsymbol{\textcolor{#32936F}{x_1}}} ) + \textcolor{#A14DA0}{\boldsymbol{b}}y1 =2(x1 )+b - and finish for b\textcolor{#A14DA0}{\boldsymbol{b}}b.If this is all amazing, Don't sweat, try step by step below

. So, remember, our equation is:y=mx+by = \textcolor{#F18F01}

{\boldsymbol{m}}x + stands for bevel and b\textcolor{#A14DA0}{\boldsymbol{b}}b stands for y-intercept of rows. Steps to write this equation if we have a point and slope below. First, let's say our slope is 2\textcolor{#F18F01}{\boldsymbol{2}}2. Plug into our equation: y=2x+by = \textcolor{#F18F01}{\boldsymbol{2}}x \textcolor{#F18F01}{\boldsymbol{2}}x

\textcolor{#A14DA0}{\boldsymbol{b}}y=2x+bNow, we'll connect our dots into the equation to solve b\textcolor{#A14DA0}{\boldsymbol{b}}b. Let's say our point is (3,5)(3, 5)(3,5):5=2(3)+b5=6+b5-6=b-1=b\begin{aligned} 5 &= \textcolor{#F18F01}{\boldsymbol{2}}(3) + \textcolor{#A14DA0}{\boldsymbol{b}} \\ 5 &= 6 + \textcolor{#A14DA0}

{\boldsymbol{b}} \\ 5 - 6 &= \textcolor{#A14DA0}{\boldsymbol{b}} \\ -1 &= \textcolor{#A14DA0}{\boldsymbol{b}} \end{aligned}555-6-1=2(3)+b=6+b=b=bNow, we have our slope and y-intercept, so we can plug them back in to get our final equation:y=2x-1y = \textcolor{#F18F01}{\boldsymbol{2}}x \textcolor{#A14DA0}{\boldsymbol{-1}}y=2x-1If this is

all overwhelming, no sweat, try it step-by-step below

. Slope Tapping Form Calculator (Two Dots)Slope Intersection Shape Calculator (Point & Near Fun is a 501(c)(3) nonprofit Made in NYC

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