Question

Which equation represents a line through points (–8, 3) and (–2, –3)?

Answer 1

(-8, 3) and (-2, -3) is y = -x - 5

Explanation:

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

Where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.

Given the points (-8, 3) and (-2, -3), we can calculate the slope (m) using the formula:

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

Substituting the coordinates into the formula:

m = (-3 - 3) / (-2 - (-8))

m = (-3 - 3) / (-2 + 8)

m = (-6) / (6)

m = -1

Now that we have the slope (m = -1) and one of the points (x1, y1) = (-8, 3), we can use the point-slope form to write the equation:

y - 3 = -1(x - (-8))

y - 3 = -1(x + 8)

y - 3 = -x - 8

y = -x - 8 + 3

y = -x - 5

Therefore, the equation that represents a line passing through the points (-8, 3) and (-2, -3) is y = -x - 5.

Hope this helped :)

Answer 2

y = -x - 5

Explanation:

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

We first need to find the slope of the line passing through the two given points. We can use the formula:

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

where (x1, y1) = (-8, 3) and (x2, y2) = (-2, -3)

m = (-3 - 3) / (-2 - (-8)) = -6 / 6 = -1

Now, we can use the point-slope form of the equation with one of the given points, say (-8, 3):

y - 3 = -1(x - (-8))

Simplifying:

y - 3 = -x - 8

y = -x - 5