Question

Write the equation of the line that passes through the points (-2,-8) and (8,8) in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

To find the equation of a line passing through two points, find the slope using the given formula and then use the point-slope form to write the equation.

Step-by-step explanation:

To write the equation of a line that passes through two given points, we can use the point-slope form of a linear equation. The point-slope form is given by the equation y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) are the coordinates of one of the points.

First, we need to find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1). For the points (-2,-8) and (8,8), the slope is m = (8 - (-8)) / (8 - (-2)) = 16 / 10 = 1.6.

Next, we can choose either of the two points, let's choose (-2, -8), and substitute it into the point-slope form: y - (-8) = 1.6(x - (-2)).

Simplifying further, we get the equation y + 8 = 1.6(x + 2).