What is an equation of the line through (-8, -4) and (4, 5)

y = 3/4x + 2

Step-by-step explanation:

We are asked to find the equation of a line with two points

Step1: find the slope

m = (y_2 - y_1)/(x_2 - x_1)

(-8 , -4) ( 4 , 5)

x_1 = -8

y_1 = -4

x_2 = 4

y_2 = 5

Insert the values into

m =( y_2 - y_1)/(x_2 - x_1)

m = ( 5 - (-4))/ ( 4 - (-8)

m = ( 5 + 4)/(4 + 8)

m = 9/12

It can be simplified by dividing by 3

= (9/3)/(12/3)

= 3/4

m = 3/4

Step 2: substitute m into the equation

y = mx + c

y = 3/4x + c

Step3: substitute either of the points

Let's pick ( 4 , 5)

x = 4

y = 5

5 = 3/4(4) + c

5 = (3 * 4)/4 + c

5 = 12/4+ c

5 = 3 + c

5 - 3 = c

c = 5 - 3

c = 2

Step 4: sub c into the equation

y = 3/4x + 2

Therefore, the equation of the line is

y = 3/4x + 2