Question

Write the equation of the line that passes through the points left bracket, minus, 5, comma, 9, right bracket(−5,9) and left bracket, 8, comma, minus, 9, right bracket(8,−9). put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

The equation of the line passing through the points (-5,9) and (8,-9) is y = (-18/13)x + 279/13 in fully simplified point-slope form.

Step-by-step explanation:

The equation of the line passing through the points (-5,9) and (8,-9) can be found using the point-slope form.

The formula for the point-slope form is:

y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point and m is the slope of the line.

First, we calculate the slope (m) using the formula:

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

Plugging in the coordinates (-5,9) and (8,-9), we have m = (-9 - 9) / (8 - (-5)) = -18 / 13.

Next, we choose one of the points (let's use (-5,9)) and substitute the values into the point-slope form equation:

y - 9 = (-18/13)(x - (-5))

Simplifying this equation gives us the fully simplified point-slope form:

y = (-18/13)x + 279/13.