Write the equation of the line that passes through (−3, -5) and (-2, 10) in slope-intercept form

y = 15x + 40

Step-by-step explanation:

(-3, -5) and (-2, 10)

First you want to find the slope of the line that passes through these points. To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)

Plug in these values:

(10 - (-5)) / (-2 - (-3))

Simplify the parentheses.

= (10 + 5) / (-2 + 3)

= 15 / 1

Simplify the fraction.

15/1

= 15

This is your slope. Plug this value into the standard slope-intercept equation of y = mx + b.

y = 15x + b

To find b, we want to plug in a value that we know is on this line: in this case, I will use the second point (-2, 10). Plug in the x and y values into the x and y of the standard equation.

10 = 15(-2) + b

To find b, multiply the slope and the input of x(-2)

10 = -30 + b

Now, add 30 to both sides to isolate b.

40 = b

Plug this into your standard equation.

y = 15x + 40

This is your equation.

Check this by plugging in the other point you have not checked yet (-3, -5).

y = 15x + 40

-5 = 15(-3) + 40

-5 = -45 + 40

-5 = -5

Your equation is correct.

Hope this helps!