How to convert standard form equations to slope intercept form
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How to convert standard form equations to slope intercept form
Recommendations Recs We can use the skills of solving for a variable to change any linear equation into slope-intercept form. All that is required is that we solve for \({\text{y}}\) then arrange them so that the term with \({\text{x}}\) in it comes first. Linear equation = an equation that is a straight line when graphed Video Source (10:29 mins) |
Transcript Remember, the key to converting a linear equation to slope-intercept form is to solve for \({\text{y}}\) using the tools we learned in PC 101 Weeks 11 and 12. Solving for a variable is used when analyzing data. Additional Resources Khan Academy: Converting to Slope-Intercept Form (05:07 mins, Transcript) Change the following equations
into the slope-intercept form of a line: \({\text{y}}+14=-4{\text{x}}\) \({\text{y}}{-}7 = \frac{1}{3}{\text{x}}\) \({\text{y}} + \frac{3}{8} = \frac{1}{8}{\text{x}}\) \({\text{x}}=\frac{{\text{y}}+36}{9}\) \(-6{\text{x}}{-}2{\text{y}}=-7\) \(3{\text{x}}{-}2{\text{y}}=-1\) If you're seeing this message, it means we're having trouble loading
external resources on our website. If you're behind a web filter, please make sure that the domains *. and *. are unblocked. Any equation that relates the first power of x to the first power of y produces a straight line on an x-y graph. The standard form of such an equation is Ax + By + C = 0 or Ax + By = C. When you
rearrange this equation to get y by itself on the left side, it takes the form y = mx +b. This is called slope intercept form because m is equal to the slope of the line, and b is the value of y when x = 0, which makes it the y-intercept. Converting from slope intercept form to standard form takes little more than basic arithmetic. To convert from slope
intercept form y = mx + b to standard form Ax + By + C = 0, let m = A/B, collect all terms on the left side of the equation and multiply by the denominator B to get rid of the fraction. An equation in slope intercept form has the basic structure y = mx + b \begin{aligned} y - mx &= (mx - mx ) + b \\ y - mx &= b \end{aligned} \begin{aligned} y - mx - b
&= b - b \\ y - mx - b &= 0 \end{aligned} -mx + y - b = 0 If m is an integer, then B will equal 1. -\frac{A}{B}x + y - b = 0 -Ax + By - Bb = 0 -Ax + By - C = 0 (1) - The equation of a line in slope intercept form is: y = \frac{1}{2} x + 5 What is the equation in standard form? y - \frac{1}{2}x = 5 y - \frac{1}{2}x - 5 = 0 2y - x - 10 = 0 -x + 2y - 10 = 0 You
can leave the equation like this, but if you prefer to make x positive, multiply both sides by -1: x - 2y + 10 = 0 x - 2y = -10 (2) - The slope of a line is -3/7 and the y-intercept is 10. What is the equation of the line in standard form? The slope intercept form of the line is y = -\frac{3}{7}x + 10 Following the procedure outlined above: \begin{aligned} y +
\frac{3}{7}x - 10 = 0 \\ 7y + 3x - 70 = 0 \\ 3x + 7y -70 = 0 \\ \text{or} \\ 3x + 7y = 70 \end{aligned} A standard form equation is when it is set up Ax + By = C. 6x + 2y = 4 A slope-intercept form equation is when it is set up y=mx+b. Y = - 3x + 2 In order to go from one form to another, all you have to do is change the order of the given numbers.
First you want to move the Ax to the opposite side of the equation, by either adding or subtracting it. At this point your equation will be set up By = -Ax + C. Then you want to divide the B from the By and the rest of the equation. Therefore you will have y = - Ax/B + C/B. This is the same thing as the slope-intercept form, just a few of the letters are
different. Example 1:
Change from standard to slope form 8x + 4y = 16 8x + 4y = 16 first subtract 8x 4y = -8x + 16 then divide all by 4 y = -2x + 4 slope form Example 2: 6x + 3y = 21 6x + 3y = 21 subtract 6x 3y = -6x + 21 then divide all by 3 y = -2x + 7 slope form The general equation or standard equation of a straight line is: \[ax +
by + c = 0\] In which, $$a$$ and $$b$$ are constants and either $$a e 0$$ or $$b e 0$$. Now to convert this linear equation in standard form to the slope intercept form, by definition the slope-intercept is written as $$y = mx + c$$. To convert the standard form to the slope intercept form, take the standard equation and separate the variable $$y$$
on the left hand side as follows: \[\begin{gathered} ax + by + c = 0 \\ \Rightarrow by = ? ax ? c \\ \Rightarrow y = \frac{{ ? ax ? c}}{b} \\ \Rightarrow y = ? \frac{a}{b}x ? \frac{c}{b} \\ \end{gathered} \] Compare this equation with the slope intercept form $$y = mx + c$$ where the slope is $$ ? \frac{a}{b}$$ and the y-intercept is $$ ? \frac{c}
{b}$$. Example: Convert the equation $$2x + 5y ? 6 = 0$$ into the slope intercept form. The equation of the line in standard form is $$2x + 5y ? 6 = 0$$ \[\begin{gathered} \Rightarrow 5y = ? 2x + 6 \\ \Rightarrow y = \frac{{ ? 2x + 6}}{5} \\ \Rightarrow y = ? \frac{2}{5}x + \frac{6}{5} \\ \end{gathered} \] Compare this with equation $$y = ?
\frac{2}{5}x + \frac{6}{5}$$ with the slope intercept form $$y = mx + c$$. Here the slope is $$ ? \frac{2}{5}$$ and the y-intercept $$\frac{6}{5}$$. The standard form equation is a linear equation that contains two variables, usually (but not limited) to x-terms and y-terms, that are on the same sides of the equation: Ax + By = C Coefficients A, B,
and C must be whole number integers that have no decimals or fractions. In the standard form equation, coefficients B and C can be positive or negative numbers, but coefficient A must be a positive number. Point-Slope, Slope-Intercept, and Standard Form Equations A linear equation is the equation of a line on a graph. Linear equations come in
different forms, like point-slope form and slope-intercept form. Let's explain each of these forms. Standard form: Writing an equation in standard form makes it easier to find the x and y-intercepts, which is where the graph crosses the x- and y-axis. All you have to do is plug in a 0 for the y to find the x-intercept or a 0 for the x to find the y-intercept.
Point-slope form: In point-slope form, x1 and y1 are coordinates of a point on a graphed line, and m is the line's slope. Slope-intercept form: The slope-intercept form has the slope, m, and the y-intercept, b, on the right-hand side of the equation. Since this is a useful form, you'll often be asked to convert an equation from standard form to slope-
intercept form. So let's show you how to do this. Converting Standard Form to Slope-Intercept Form Let's convert the following standard form equation to slope-intercept form: We want to isolate the y, so let's start by subtracting 6x from both sides: As you can see, you're left with -2y on the left. Now, we must divide both sides by -2 to isolate the y:
Once you rearrange this equation to be in the y = mx + b format, this equation is in slope-intercept form: How to Convert Standard Form Equations As we've stated, in standard form, equations coefficients A, B, and C must be whole numbers. Let's convert the below equation, which contains fractions and negative numbers, into a proper standard
form equation: The first step is removing the fractions from the equations. To do this, we must determine the common factors of the two denominators, -4 and 8. The least common denominator of these two numbers is 8, so let's multiple each side by this: Now that all the coefficients in this equation are whole numbers, we need to convert -6 into a
positive number. We can do this by multiplying both sides of the equation by -1: Learning How to Write Standard Form Equations Standard form is one of the three different ways to write linear equations. Finding common factors to convert equations with fractions into standard form equations makes it easier to move onto more complex math
concepts, like graphing linear equations. More Math Homework Help
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