Question

What is the equation of the line that passes through (-1,-2) and (3,10)?

4x−y=−2

4x−y=2

3x−y=1

3x−y=−1

Answer 1

The first step is to find the slope of the line. The slope (m) is given by:

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

Using the points (-1,-2) and (3,10):

m = (10 - (-2)) / (3 - (-1))
m = 12 / 4
m = 3

So the slope of the line is 3.

Next, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (-1,-2):

y - (-2) = 3(x - (-1))
y + 2 = 3(x + 1)
y + 2 = 3x + 3
y = 3x + 1

So the equation of the line that passes through (-1,-2) and (3,10) is 3x - y = 1.

Therefore, the correct answer is 3x - y = 1.