Question

Write the equation of the line that passes through the points left bracket, minus, 9, comma, minus, 9, right bracket(−9,−9) and left bracket, minus, 8, comma, 1, right bracket(−8,1). 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 (-9, -9) and (-8, 1) is y + 9 = 10(x + 9).

Step-by-step explanation:

The equation of the line passing through the points (-9, -9) and (-8, 1) can be found using the point-slope form:

y - y1 = m(x - x1)

where (x1, y1) are the coordinates of one of the given points, and m is the slope. First, we calculate the slope using the formula: m = (y2 - y1) / (x2 - x1). Substituting the values (-9, -9) and (-8, 1) into the formula gives: m = (1 - (-9)) / (-8 - (-9)), which simplifies to m = 10 / (-8+9) = 10 / 1 = 10.

Next, we choose one of the given points, for example (-9, -9), and substitute it into the point-slope form, along with the slope: y - (-9) = 10(x - (-9)). Simplifying this equation gives the fully simplified point-slope form of the line passing through the two given points as: y + 9 = 10(x + 9).