Question

Write an equation of the line passing through each of the following pairs of points:
(−10, 4), (2, −5)

Answer 1

Answer:

$y=-\frac{3}{4}x-\frac{7}{2}$

Step-by-step explanation:

To find the equation of a line that passes through the points (-10, 4) and (2, -5), let's first find the slope.

The formula for slope is:

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

Let's let (-10, 4) be (x₁, y₁) and let's let (2, -5) be (x₂, y₂). Substitute this into the slope formula:

$m=\frac{-5-4}{2-(-10)}$

Simplify:

$m=\frac{-5-4}{2+10}$

Add or subtract:

$m=-9/12$

Reduce:

$m=-3/4$

Now that we know the slope, we can use the point-slope form to find the equation of our line. The point-slope form is:

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

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

Let's substitute -3/4 for m. Let's also use (-10, 4) be (x₁, y₁) for consistency. So:

$y-4=-\frac{3}{4}(x-(-10))$

Simplify:

$y-4=-\frac{3}{4}(x+10)$

Distribute:

$y-4=-\frac{3}{4}x-\frac{30}{4}$

Add 4 to both sides:

$y=-\frac{3}{4}x-\frac{30}{4}+\frac{16}{4}$

Add:

$y=-\frac{3}{4}x-\frac{14}{4}$

Reduce:

$y=-\frac{3}{4}x-\frac{7}{2}$

And that's our equation.

And we're done!

Answer 2

x= (-10,4) and x= (2, -5)