Question

Write the equation of the line that passes through the points (-3,-8) and (-9,9) in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

The equation of the line passing through (-3,-8) and (-9,9) in point-slope form is y + 8 = (-17/6)(x + 3).

Step-by-step explanation:

In order to write the equation of the line that passes through the points (-3,-8) and (-9,9) in point-slope form, we must first calculate the slope using the formula:

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

Substituting the given points, we have:

slope = (9 - (-8)) / (-9 - (-3)) = 17 / -6 = -17/6

Next, we can choose either point to plug into the point-slope form equation:

y - y1 = m(x - x1)

Using the point (-3,-8):

y - (-8) = (-17/6)(x - (-3))

Simplifying further, we get the equation:

y + 8 = (-17/6)(x + 3)

This is the equation of the line that passes through the given points.