slope-intercept form linear functions. y = mx + b slope - measure of the steepness of a line...

SLOPE-INTERCEPT FORM

LINEAR FUNCTIONS

y = mx + b

Slope - measure of the steepness of a line

y-intercept - where the line crosses the y-axis

First let’s practice with the slope.

4

5

This line has a slope of 4/5. It shows a rise of 4 and a run of 5.

Slope = riserun

This line has a slope of 4/5.

Or use the formula:

m = y2 y1

x2 x1(2,1)

(-3,-3)

3 1 3 2

4

5

4

5

-6

5

Note this line has a negative slope. m = - 5 / 6

positive slope negative slope

No slope Slope is 0

Now you tell what kind of slope each of the following lines have. Click the

mouse to check your answer.

positive

positive

No slope

negative

zero

negative

positive

negative

Now let’s look at the y-intercept.

This line intercepts the y-axis at 2 so in the slope intercept form, the b = 2.

Name the y-intercept. Click to check

b = -3

b = 2

b = 3.5

b = 0

Now let’s combine the slope and the y-intercept to write the equation of the line shown.

-6

3

m = 3 /- 6

or

m = -.5

b = 1

y = mx + b

y = -.5x + 1

6

3 m = 6 / 3

or

m = 2

y = 0

y = mx + b

y = 2x + 0

y = 2x

m = 0

b = - 2

y = mx + b

y = 0x + (-2)

y = -2

No slope

No y-intercept

x = -1

Special case:

x = 3

Your turn. Click mouse to check

y = 3x + 1

y = 3x

y = - 1/3 x - 1

x = -3

y = -4/3 x

y = 4

But what do you do if the y-intercept is not a whole number?

(3,-4)

(-3,1)

Use any 2 points on the line to find the slope.

(3,-4)

(-3,1)

m 4 1

3 3

m 5

6

Then use that slope and either of the 2 points to find the y-intercept.

ymx b

4 5

6(3) b

4 5

2 b

11

2b

(3,-4)

(-3,1)m = -5/6

b = -1 1/2

y= mx + b

y = -5/6x - 1 1/2

Try the next one…

y = 4x - 8

When you have the equation of the line, any point on the line will make the equation a true statement. This is a good way to check your equation.