Question

What is an equation of the line that passes through the points left bracket, 4, comma, 8, right bracket(4,8) and left bracket, minus, 2, comma, minus, 7, right bracket(−2,−7)?
Answer
Attempt 1 out of 2

Answer 1

To find the equation of the line that passes through the points (4, 8) and (-2, -7), we can use the point-slope form of the equation, which is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is one of the points on the line.

First, let's find the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (-7 - 8) / (-2 - 4)
m = -15 / -6
m = 2.5

Now, let's choose one of the points, say (4, 8), and substitute the values into the point-slope form equation:

y - 8 = 2.5(x - 4)

Simplifying:

y - 8 = 2.5x - 10

Now, let's rearrange the equation to solve for y:

y = 2.5x - 10 + 8
y = 2.5x - 2

Therefore, the equation of the line that passes through the points (4, 8) and (-2, -7) is y = 2.5x - 2.