Lesson: Graphing in Point-Slope Form

Multiple Choice

Do you have your phone in the box, notebook out, and ready to take notes? ​

(you will need to take a picture and upload it at the end)

• YES I have my notebook out

• No, I know it means a bad grade

Graphing in
Point-Slope Form

Objective: Graph​ Equations written in Point-Slope Form

Graphing

WARM-UP: Graph $$y=\frac{1}{4}x-3$$

Slope Intercept REVIEW

EXAMPLE

We can graph ANY line as long as we have a starting point and the slope.

​

Graph the line that goes through the point (-2,3) and has a slope of -4 .

Graphing

Graph the line that goes through the point (-2,-4) 

and has a slope of  $$\frac{3}{4}$$ . 

Point-Slope Form

The SLOPE is easy to identify.

The POINT is a little trickier.

​

First, the y-coordinate (y₁) is first.

And the x-coordinate (x₁) is second.

So we have to reverse the numbers

​AND the sign for (x,y) is opposite.

​

(easier to explain with an example)

​y - y₁ = m(x - x₁)

Slope: m

Point: (x₁,y₁)

EXAMPLES

Given the equation: y - 4 = -2(x - 3), identify the slope and the point on the line.​

​y - y₁ = m(x - x₁)

Point: (-5,3)

Multiple Select

Given the equation: $$y+9=\frac{2}{5}(x-5)$$ , identify the slope and point of the line.

• Slope:  $$\frac{2}{5}$$  

• Point: (5,-9)

• Point: (-5,9)

• Point: (9,-5)

• Point: (-9,-5)

EXAMPLE​

Graph: y - 3 = -2(x + 1)

Graphing

Graph:  $$y+1=-\frac{1}{3}(x-2)$$