Question

Write an equation of the line that passes through a pair of points:

(-5,-2), (4,5)
It’s not b

Answer 1

C

Explanation:

We want to determine the equation of the line that passes through the points (-5, -2) and (4, 5).

First, let’s determine the slope of the line. We can use the slope formula:

`\displaystyle m=(y_2-y_1)/(x_2-x_1)`

Let (-5, -2) be (x₁, y₁) and let (4, 5) be (x₂, y₂). Substitute appropriately:

`\displaystyle m=(5-(-2))/(4-(-5))`

Evaluate:

`\displaystyle m=(5+2)/(4+5)=(7)/(9)`

So, our slope is 7/9.

Now, we can use the point-slope form to determine the rest of the equation:

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

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

So, we will substitute 7/9 for m.

For consistency, we will also let (x₁, y₁) be (-5, -2). Hence:

`\displaystyle y-(-2)=(7)/(9)(x-(-5))`

Simplify:

`\displaystyle y+2=(7)/(9)(x+5})`

Distribute:

`\displaystyle y+2=(7)/(9)x+(35)/(9)`

Subtract 2 from both sides. Note that 2 is equivalent to 18/9. Hence:

`\displaystyle y=(7)/(9)x+(35)/(9)-(18)/(9)`

Simplify:

`\displaystyle y=(7)/(9)x+(17)/(9)`

Therefore, our answer is C.