Writing Equations of Lines

Slope – Intercept Form

To write an equation of a line in slope-intercept form, you need …

… the y-intercept

… The Slope

b

m

Once you have these two things, you can write the equation as

y = m x + b

DONE

y = -2 x + 5

Write the equation of the line that slope -2 and y-intercept 5.

Example #1

y = m x + bStarting with the slope –intercept form

Plug in the slope, and the y –intercept to get

DONE

y – y1 = m (x – x1)

… The Slope …

… Any Point On The Line

Point – Slope FormTo write an equation of a line in point – slope form, all you need is …

(x1, y1)

m

Once you have these two things, you can write the equation as

DONE

Example #1Write the equation of the line that goes through the point (2, –3) and has a slope of 4.

Point = (2, –3)

Slope = 4

y – y1 = m (x – x1)

y + 3 = 4 (x – 2)

Starting with the point – slope form

Plug in the y-value, the slope, and the x-value to get

Notice, that when you subtracted the “–3” it became “+3”.

DONE

y – 6 = (x + 4)32

y – y1 = m (x – x1)

Example #2

Starting with the point – slope form

Plug in the y-value, the slope, and the x-value to get

Notice, that when you subtracted the “–4” it became “+4”.

Point = (–4, 6)

Slope = 32

DONE

32

Write the equation of the line that goes through the point (–4, 6) and has a slope of .

To use point – slope form, we need a point and a slope. Since we have two points, just pick one … IT DOESN’T MATTER … BOTH answers are acceptable… let’s see why:

We have two points, but we’re missing the slope. Using the formula for slope, we can find the slope to be

Write the equation of the line that goes through the points (6, –4) and (2, 8) .

Example #3

Point = (6, –4)

Slope = –3

y + 4 = –3 (x – 6)

Point = (2, 8)

Slope = –3

y – 8 = –3 (x – 2)

Using the first point, we have, Using the second point, we have,

DONE

34

12

x

ym

Writing Equations in Slope – Intercept Form

y + 4 = –3 (x – 6) y – 8 = –3 (x – 2)

Distribute Distribute

y + 4= –3x + 18 y – 8 = –3x + 6

Subtract 4 and combine like terms

Add 8 and combine like terms

y = –3x + 18 – 4

y = –3x + 14

y = –3x + 6 + 8

y = –3x + 14

Notice … They’re the same!

DONE

Horizontal Line: y = c , where c is a constant. Example: y = 3

Other Forms of Linear Equations

DONE

1 2 43

5

-1-2-3-4-5

1

2

3

4

5-1

-2-3

-4

-5

Vertical Line: x = c , where c is a constant. Example: x = 2

Other Forms of Linear Equations

DONE

1 2 43

5

-1-2-3-4-5

1

2

3

4

5-1

-2-3

-4

-5

Your turn:Write the equation of the line described in slope-intercept form

1.Has slope -5 and y-intercept 3

2.That contains the point (6, 2) and has slope

3.That contains (-2, -4) and has slope

4.That contains the points (4, 5) and (6, 12)

5.That contains the points (-1, 2) and (5, -4)

6.That is vertical and contains (3, 8)

7.That is horizontal and contains (2, -7)

23

DONE

8

1

HW Write all equations in slope-intercept form

pg. 304 #10 to 30 even

DONE