Section 4 7 SlopeIntercept Form Coordinated Plane Graphing

Section 4. 7 Slope-Intercept Form

Coordinated Plane

Graphing Lines • A line is the graph of a linear equation in the form. • This is called the Slope-Intercept form of the line because: – m is the slope and – b is the y-intercept.

Identifying the slope and y-intercept y = 2 x + 1 y = -2 x m=2 m = -2 b=1 b=0 y = 5 x - 3 m=5 b = -3

Your Turn y = 12 x - 15 m = 12 b = -15 y = -4 x m = -4 b=0 b=4

Putting into Slope-intercept • You can only find the slope and y-intercept if the equation is in slope-intercept form. • If it is in any other form you need to solve for y.

Solving for y 2 x + 3 y = 6 -2 x 3 y = -2 x + 6 3 3

Your Turn 5 x + 3 y = 15 -5 x 3 y = -5 x + 15 3 3

Writing the Equation of a Line • To write the equation of a line, you must know the slope, m, and the y-intercept, b. • If it is in the form of y =mx + b, you have both the slope and the y-intercept. • If it is not in slope-intercept form, you need solve for y in order to find m and b.

Graphing Lines • Plot the y-intercept on the y-axis. • Obtain a second point by using the slope, starting from the y-intercept. • If the slope is positive go up if it is negative go down, going the same number of spaces as the top number. • Then go to the right or positive direction the same number of spaces as the bottom number. • Use a straightedge to connect the dots. • Remember – A line continues infinitely in both directions, so put arrows on the end of your lines.

Example 1 • Graph y = 2 x+1. m = 2/1 b=1

Example 2 b = -2

Your Turn • Graph y = 3 x + 2 • m = 3/1 • b=2

Example 3 4 x + 2 y = 6 -4 x 2 y = -4 x + 6 2 2 y = -2 x + 3 m = - 2 = -2/1 b=3

Your Turn 6 x - 3 y = 9 -6 x -3 y = -6 x + 9 -3 -3 y = 2 x - 3 m = 2/1 b=-3