What is an equation of the line that passes through the points (−4,2) and (−8,−3)?

Answer 1

a line through (-4,2) and (-8,-3) has slope = (2+3)/(-4+8) = 5/4 = (y-2)/(x+4)

cross multiply

5x +20 = 4y-8

5x -4y =-28

Answer 2

Hello Ruby,

We will use the equation of a line in the form

y = mx + b

and solve for the value of the constants m and b.

m is the slope of the line and b is the y-intercept (point on the y axis where the line cross the y axis),

First we will solve for m. Then we will use the value of m and substitute the x and y values of one of the points and solve for b.

We can then check our answer by using the x-value for point 2 and check that the equation gives us the y-value of point 2.

The slope is equal to the change in y divided by the change in x

m = (y₁ - y2)/(x₁ - x₂)

It does not matter which point we call point 1 and point 2. We just have to be consistent when applying them to the equation to calculate the slope.

Let point 1 be (-4, 2)

and then

point 2 is (-8,-3)

So using our equation for slope we get

m = (y₁ - y2)/(x₁ - x₂) = (2 - (-3))/(-4 - (-8)) = (2 + 3)/(-4 + 8) = 5/4

Now substitute the value for m in the equation and the values of x and y for either point 1 or point 2 and solve for the intercept b.

In this case I will use point 1.

y = mx + b

2 = (5/4)(-4) + b

2 = -5 + b

adding 5 to both sides we get

7 = b

So the slope intercept form of this line is

y = (5/4) x + 7

Now, we can check this answer by using the x-value for point 2 and check that it gives the y-value for point 2.

y = (5/4) (-8) + 7

y = -10 + 7 = -3

and -3 is the y value for point 2. So, the answer is correct.

I hope this helps.

Please contact me if you have any questions.

Best Regards,

Dean