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.

bmxy +=

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

42

3+= xy

m = 12

b = -15

m = -4

b = 0

2

3=m

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 -2x

3y = -2x + 63 3

23

2+

−= xy

Your Turn

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

3y = -5x + 153 3

53

5+

−= xy

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

23

2−−= xy

3

2−=m

b = -2

Your Turn

• Graph y = 3x + 2

• m = 3 = 3/1

• b = 2

Example 3

4x + 2y = 6-4x -4x2y = -4x + 62 2

y = -2x + 3

m = - 2 = -2/1

b = 3

Your Turn

6x - 3y = 9-6x -6x-3y = -6x + 9-3 -3

y = 2x - 3

m = 2 = 2/1

b = - 3