Question

Write an equation of the line passing through each of the following pairs of points:

(−10, 4), (2, −5)

Answer 1

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

Answer 2

`y=-(3)/(4)x-(7)/(2)`

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=(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=(-5-4)/(2-(-10))`

Simplify:

`m=(-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=-(3)/(4)(x-(-10))`

Simplify:

`y-4=-(3)/(4)(x+10)`

Distribute:

`y-4=-(3)/(4)x-(30)/(4)`

Add 4 to both sides:

`y=-(3)/(4)x-(30)/(4)+(16)/(4)`

Add:

`y=-(3)/(4)x-(14)/(4)`

Reduce:

`y=-(3)/(4)x-(7)/(2)`

And that's our equation.

And we're done!