# Section 4.7 Slope-Intercept Form. Coordinated Plane.

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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 = 2x + 1 m = 2 b = 1 y = 5x - 3 m = 5 b = -3 y = -2x m = -2 b = 0

Your Turn y = 12x - 15 y = -4x m = 12 b = -15 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 2x + 3y = 6 -2x 3y = -2x + 6 33

Your Turn 5x + 3y = 15 -5x 3y = -5x + 15 33

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 = 2x+1. m = 2 = 2/1 b = 1

Example 2 b = -2

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

Example 3 4x + 2y = 6 -4x 2y = -4x + 6 22 y = -2x + 3 m = - 2 = -2/1 b = 3

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