Question

What equation in slope-intercept form represents the line that passes through the points (3, –2) and (1, –3)?

Answer 1

To find the equation in slope-intercept form, we need to determine the slope and the y-intercept of the line.

We can find the slope (m) using the formula:

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

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

m = (-3 - (-2)) / (1 - 3)
= (-3 + 2) / (1 - 3)
= -1 / -2
= 1/2

The slope is 1/2.

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

y - y1 = m(x - x1)

Using the point (3, -2) and the slope m = 1/2, we have:

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

Simplifying:

y + 2 = 1/2x - 3/2

Subtracting 2 from both sides:

y = 1/2x - 3/2 - 2
= 1/2x - 7/2

The equation in slope-intercept form that represents the line passing through the points (3, -2) and (1, -3) is:

y = 1/2x - 7/2