Aim: What is the equation of a line?

Do Now: Find the slope of the line 8x + 5y = 20

x + 4

This is the slope – intercept form

y = mx + b

HW: Handout

8x + 5y = 20 is the called general form

We use the notation Ax + By + C = 0 for general form of a line

What is the slope formula? 𝑚=𝑦2− 𝑦1

𝑥2− 𝑥1

We can change the general form to slope-intercept form by solving for y

, where is the slope

If we cross-multiply 𝑚=𝑦2− 𝑦1

𝑥2− 𝑥1

𝑦 2− 𝑦1=𝑚 (𝑥2 −𝑥1)

This is called point-slope form

To write the equation of a line if the slope and one point are known, just plug in the coordinates of the point and slope into= )

Summary of the equation of a line

I. slope-intercept form y = mx + b

II. General form Ax + By + C = 0

III. Slope-point form )

Things to remember

If two lines are // then their slopes are equal

If two lines are perpendicular then their slopes are negative reciprocal

Horizontal line whose slope is 0Vertical line whose slope is undefined

Drill1. Find if A(1,2) and B(-1,-3)2. Find m of the line // to if A(1,-2) B(2,1)3. Write an equation of the vertical and

horizontal line through (2,3)4. Write an equation of the line through

(1,1) with m = 35. Write an equation of the line with m = -2

y-intercept = -16. Write an equation of the line through the

points (3,1) and (-5,2)