Question

Write the equation of the line that passes through the points (4,−2) and (6,3). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

To find the equation of a line that passes through two given points, we can use the point-slope form of a line.

The first step is to find the slope of the line. We can do this by using the formula:

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

Plugging in the values for the two given points:

m = (3 - (-2)) / (6 - 4) = 5 / 2

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

y - y1 = m (x - x1)

Plugging in the values we have:

y - (-2) = 5/2 (x - 4)

Expanding the right side:

y + 2 = 5/2 x - 4

Multiplying both sides by 2:

2y + 4 = 5x - 8

Adding 8 to both sides:

2y + 12 = 5x

Dividing both sides by 2:

y + 6 = 2.5x

So the equation of the line that passes through the points (4, -2) and (6, 3) is y + 6 = 2.5x.