Question

Figure this out for me pls

Answer 1

D

Explanation:

Well we can break this problem into 2 major steps:

Finding the slope

and

Substituting a value

So let's begin!

Finding the slope

We know that for our slope-intercept equation y=mx+b, m is our slope and our b is the y-intercept. To get the slope, we use the rate of change, or really the change in y-values divided by the corresponding x-values.

Meaning of the points (1,2) and (3,4) we would solve for the slope like this:

`(4-2)/(3-1) = (2)/(2) = 1\\`

1 is our slope in this example.

Similarly in this problem we have the points (-5, -7) and (4, 8)

`(8-(-7))/(4-(-5)) = (15)/(9)`

We now know that
`(5)/(3)` is our slope after we simplify the fraction.

Substituting a value

To reiterate, we know that the slope-intercept equation is y = mx + b where b is our y-intercept and m is our slope.

To substitute our slope we would get:

`y=(5)/(3)x +b`

Using a value, suppose (4,8), we substitute 4 for x and 8 for y as is logical given our coordinate points.

`8=(5)/(3)(4) +b`

Simplifying we get:

8 = 20/3 + b

24/3 = 20/3 + b

b = 24/3 - 20/3

`b = (4)/(3)`

Thus we have gotten our answer as 4/3 which is option D on your screen.