Graphing Linear Equations In Slope-Intercept Form

In order to graph using point plotting, you will need to create a table. You will need to choose at least 3 numbers for x and “plug” them into the equation to find corresponding y values. For Example: Graph y = 2x - 1 xyxy Choose x values “ plug” x into the equation Plot the points 2(-1)-1=-3 02(0)-1 = -1 12(1)-1 = 1

Graph using point plotting xyxy (-2) + 3 = 2 (0) + 3 = 3 (2) + 3 = 4

These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.

Just by looking at an equation in this form, we can draw the line (no tables). The constant is the y-intercept. The coefficient is the slope. Constant = 1, y-intercept = 1. Coefficient = 2, slope = 2. Constant = -4, y-intercept = -4. Coefficient = -1, slope = -1. Constant = -2, y-intercept = -2. Coefficient = 3/2, slope = 3/2.

The formula for Slope-Intercept Form is: ‘b’ is the y-intercept. ‘m’ is the slope. On the next three slides we will graph the three equations: using their y-intercepts and slopes.

1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y- intercept = 1. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1. up 2 right 1 up 2 right 1

1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y- intercept = -4. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1. right 1 down 1 right 1 down 1

1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y- intercept = -2. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2. right 2 up 3 right 2 up 3

Sometimes we must solve the equation for y before we can graph it. The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.

1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y- intercept = 3. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1. right 1 down 2 right 1 down 2

Important!!! This is one of the big concepts in Algebra. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept

Graphing Using the Slope-Intercept Form

To graph a linear equation, you will need to find the slope and the y-intercept for the equation. Remember: y = mx + b slope Y-intercept (the point where the graph crosses the y-axis)

Graph Slope = Y-intercept = 1. Plot the y-intercept 2.Use the slope to find the next point Slope = “rise over run”

Graph 2x + 5y = 10 using the slope-intercept form: (put the equation in slope-intercept form first) 2x + 5y = 10 5y = 10 – 2x y = 2 – 2/5 x slope = -2/5 y – intercept = 2 A negative slope means you will go down then right from the y-intercept