Question

Find the equation (in terms of x) of the line through the points (-1,-7) and (2,-1)?

a) y=2x−5
b) y=−2x+5
c) y=2x+5
d) y=−2x−5

Answer 1

The equation of the line through the points (-1,-7) and (2,-1) is found by first calculating the slope, then using the point-slope formula. The correct equation is y = 2x - 5, which corresponds to option (a).

Step-by-step explanation:

To find the equation of the line that passes through the points (-1,-7) and (2,-1), we first must calculate the slope (m) using the formula:

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

Substituting the given points:

m = (-1 - (-7)) / (2 - (-1)) = 6 / 3 = 2

Now that we have the slope, we use the point-slope formula to find the equation of the line:

y - y1 = m(x - x1)

Using the point (-1, -7):

y - (-7) = 2(x - (-1))

Simplifying:

y + 7 = 2x + 2

Subtracting 7 from both sides:

y = 2x - 5

So, the correct equation of the line is

y = 2x - 5

Hence, option (a) is the correct answer.