Question

Write an equation of the line that passes through a pair of points:
(-5,-2), (4,5)
It’s not b

Answer 1

Answer:

C

Step-by-step 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:

$\displaystyle m=\frac{y_2-y_1}{x_2-x_1}$

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

$\displaystyle m=\frac{5-(-2)}{4-(-5)}$

Evaluate:

$\displaystyle m=\frac{5+2}{4+5}=\frac{7}{9}$

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:

$\displaystyle y-(-2)=\frac{7}{9}(x-(-5))$

Simplify:

$\displaystyle y+2=\frac{7}{9}(x+5})$

Distribute:

$\displaystyle y+2=\frac{7}{9}x+\frac{35}{9}$

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

$\displaystyle y=\frac{7}{9}x+\frac{35}{9}-\frac{18}{9}$

Simplify:

$\displaystyle y=\frac{7}{9}x+\frac{17}{9}$

Therefore, our answer is C.