Question

20 points

A line goes through the points (8,9) and (-2,4)


(B) Write the equation of the line in point-slope form. Show your work.


Please only answer if you know the answer.

Please explain. :)

Answer 1

Answer:

$\displaystyle y-9=\frac{1}{2}(x-8)\text{ or } y-4=\frac{1}{2}(x+2)$

Step-by-step explanation:

Point-slope form is given by:

$\displaystyle y-y_1=m(x-x_1)$

Where (x₁, y₁) is a point and m is the slope.

So, first, we will find the slope using the two points (8, 9) and (-2, 4). We can use the slope formula:

$\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{4-9}{-2-8}=\frac{-5}{-10}=\frac{1}{2}$

Next, pick either of the two points and substitute it into the point-slope formula. Using (8, 9), we acquire:

$\displaystyle y-9=\frac{1}{2}\left(x-8\right)$

And using (-2, 4), we acquire:

$\displaystyle y-4=\frac{1}{2}\left(x -(-2)\right)\Rightarrow y-4=\frac{1}{2}\left(x+2\right)$

Both of these are valid answers.

Answer 2

Answer:

y-9=1/2(x-8)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-9)/(-2-8)

m=-5/-10

m=1/2

y-y1=m(x-x1)

y-9=1/2(x-8)