Point-Slope Form in Context

Point-Slope Form

Point-Slope Equations need 2 things....

• A point

• A slope

Multiple Choice

Which of these is point-slope?

• $$y-y_1=m\left(x-x_1\right)$$

• $$y=mx+b$$

• $$Ax+By=C$$

Multiple Choice

Write an equation of the line going through the point (-4, 1) with a slope of 1/3.

• $$y-1=\frac{1}{3}\left(x+4\right)$$

• $$y+4=\frac{1}{3}\left(x-1\right)$$

• $$y-4=\frac{1}{3}\left(x+1\right)$$

• $$y+1=\frac{1}{3}\left(x-4\right)$$

Fill in the Blanks

Name the slope of this line:

$y+1=-\frac{5}{4}\left(x-3\right)$  

Fill in the Blanks

Name the point given in this line: $y+1=-\frac{5}{4}\left(x-3\right)$  

Fill in the Blanks

Find the x-value of the point given in the equations

Student A: y - 3 = 4 (x + 2)

Student B: y + 1 = 6 (x - 5)

Student C: y + 4 = -3 (x + 8)

The sum of the three answers is

What if I'm given just 2 points?

• Use the slope formula to calculate the slope

•  $\frac{y_2-y_1}{x_2-x_1}$  

• Choose ONE of the points

• Substitute the values of your chosen point and the slope calculated into the Point-Slope form

Fill in the Blanks

What is the slope of a line passing through the points (-2, -3) and (4, 3)

Multiple Choice

Write the equation in point-slope form for the line that contains the points

(-2, -3), (4, 3)

• y - 3 = 1(x - 2)

• y + 3 = 1(x + 2)

• y -3 = -1(x + 2)

• y + 3 = -1(x - 2)

We also learned how to transform Point-Slope equations into Slope Intercept form.

Poll

Is this slope intercept form?

$$2y\ =4x\ +10$$  

• yes because it's $$y=mx+b$$  

• no, because there is a coefficient on the y.  You need to divide the entire equation by 2 first in order to get  $$y=mx+b$$  

Fill in the Blanks

Transform this point-slope equation into slope intercept form:

$y-2=3\left(x+4\right)$  

Poll

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