12-1 Study Guide – Graphing Linear Equations



Study Guide – Linear Equations & Graphing

3 Forms of Linear Equations

slope intercept form [pic] [pic]slope [pic] [pic]- intercept

point slope form [pic] [pic]slope [pic] any point on the line

standard form [pic] where [pic] Integers and [pic]

[pic] have a common factor of 1.

Slope of a Line Characteristics of Slope

[pic] [pic] [pic] [pic] [pic]

[pic] [pic]

increasing decreasing [pic]constant [pic]constant

**Parallel lines have the same slope.

**Perpendicular lines have slopes that are negative reciprocals of each other.

If two lines are perpendicular, [pic], except when the lines are horizontal or vertical.

The line perpendicular to a horizontal line is vertical. The line perpendicular to a vertical line is horizontal.

x and y intercepts

x intercept – the point where the line crosses the x axis [pic]

To find the x intercept, substitute zero for y in the equation and solve for x.

y intercept – the point where the line crosses the y axis [pic]

To find the y intercept, substitute zero for x in the equation and solve for y.

▪ When lines are vertical, there is no y-intercept and the slope is undefined. (The exception is the line x = 0 which coincides with the y-axis so it has an infinite number of y-intercepts.)

▪ When lines are horizontal, there is no x-intercept and the slope is zero. (The exception is the line

y = 0 which coincides with the x-axis so it has an infinite number of x-intercepts.)

▪ If the x-intercept and the y-intercept are the same point, (0, 0), then graphing using the intercepts is not helpful. You will need to find another point on the line or use the slope to graph.

EX 1 Find the x- and y-intercepts and identify the slope for each of the following equations.

a) 6x + 4y = -24 b) y + 5 = x c) x = 7 d) y = - 3 e) y + 2 = 3(x – 1)

Graphing Misconception Many think that if you are given the equation of a line and asked to graph that

line, you must rewrite the equation in slope intercept form to graph. NOT TRUE!!!

Graphing Lines

Two Point Method Point Slope Method

Given any two points: Given any point and the slope:

1. graph points 1. graph the point

2. draw the line through the points 2. from that point, apply the slope in

fraction form [pic]

What is the easiest way to graph a line if you are given an equation in:

slope intercept form [pic] [pic]slope [pic] [pic]- intercept

▪ Use the point slope method. Use the point [pic] and apply the slope.

point slope form [pic] [pic]slope [pic] any point on the line

▪ Use the point slope method. Use the point [pic] and apply the slope.

standard form [pic]

▪ Use what is sometimes called the intercept method. Find the x and y-intercepts, and use the two point method. Remember if only an x-intercept can be found, you will draw a vertical line through the x-intercept. If only a y-intercept can be found, you will draw a horizontal line through the

y-intercept.

Remember you can also find the x and y-intercepts of a linear equation in any form and use the two point method to graph.

Another alternative to use if given a linear equation in any form is to create an x, y table and plot the points you have found.

EX 2 Graph

a) 4x - 7y = 28

b) y = -3x + 1

c) y – 1 = [pic](x + 4)

Ex 3 Explain what points or slope you would use to graph the following.

(Remember you only need two points or a point and the slope to graph!)

| a) the line parallel to y = 2x + 1 and through |b) the line perpendicular to 3x + y= 9 and through |

|the point (1, 4) |the point (- 3, 2). |

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undefined slope

(no slope)

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