4-3 Point-Slope Form

4-3 Point-Slope Form

Multiple Choice

Recall: Which of these formulas helps you calculate the SLOPE of a line?

This is the slope formula. Stare at it. Memorize it.

Open Ended

 $\frac{y-y_1}{x-x_1}=m$  

Google thinks this is also the slope formula. Do you agree? Why or why not?

Let's rearrange this equation into another equation called "Point-Slope Form."

Multiple Choice

 $\left(x-x_1\right)\ \frac{y-y_1}{x-x_1}=m\left(x-x_1\right)$ 

What do you think will happen when we multiply both sides of the equation by (x - x₁)?

• It will make this formula way more complicated.

• It will cancel out with the denominator (bottom of the fraction).

• We will have to multiply (x - x₁) with y - y₁

This is the point-slope formula!

How to write the equation of a line in point-slope form:

• Substitute the slope in place of m

• Substitute the given point in place of x₁ and y₁

Example: What is the point-slope equation of a line with slope of -1 and through point (3,-2)?

• Substitute -1 for m

• Substitute 3 for x₁ and -2 for y₁

• If there's any "double negatives," rewrite those as +

Multiple Choice

What is the point-slope form equation of a line with slope 4 and through point (5,10)?

• y + 10 = 4(x + 5)

• y + 10 = 4(x - 5)

• y - 10 = 4(x - 5)

• y - 5 = 4(x - 10)

Multiple Choice

What is the point-slope form equation of a line with slope -1/2 and through point (3,7)?

• y - 7 = -1/2(x - 3)

• y + 7 = -1/2(x - 3)

• y + 3 = -1/2(x + 7)

• y - 3 = -1/2(x - 7)

Multiple Choice

What is the point-slope form equation of a line with slope 5 and through point (-1,9)?

• y - 1 = 5(x + 9)

• y + 9 = 5(x - 1)

• y + 1 = 5(x - 9)

• y - 9 = 5(x + 1)

What if...they don't give you the slope???

Open Ended

What if we just had two points, (0, -2) and (3, 4). Do you think could we still figure out the point-slope form equation? If so, how?

Multiple Choice

Given points (0,-2) and (3,4), what's the correct way to calculate the slope?

• $\frac{4-2}{3-0}=\frac{2}{3}$

• $\frac{4--2}{3-0}=\frac{6}{3}=2$

• $\frac{3-0}{4--2}=\frac{3}{6}=\frac{1}{2}$

• $\frac{3-0}{4-2}=\frac{3}{2}$

Now that we found the slope, we can substitute m with 2:

y - y₁ = 2 (x - x₁)

Multiple Select

We were given the points points (0,-2) and (3,4). Which one do you want to plug in?

• (0,-2)

• (3,4)

Two given points: (0, -2) and (3, 4), so there are two possible equations! Both are correct. 😃

• y - -2 = 2 (x - 0)

• y - 4 = 2 (x - 3)

Summary: If you have two points...

• Calculate the slope the slope formula. This will be your m.

• Choose either of the two points to plug in for x₁ and y₁.

Complete the "Alg 1: 4-3 Point Slope" assignment.