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

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

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)

Answer 2

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

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=(\Delta y)/(\Delta x)=(4-9)/(-2-8)=(-5)/(-10)=(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=(1)/(2)\left(x-8\right)`

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

`\displaystyle y-4=(1)/(2)\left(x -(-2)\right)\Rightarrow y-4=(1)/(2)\left(x+2\right)`

Both of these are valid answers.