Question

A given line passes through the points (-4,-4) and (-8,17). what's the equation of a line that is parallel to the given line that passes through the point (20,11)?

Answer 1

To find the equation of a line parallel to the given line (-4,-4) and (-8,17) that passes through the point (20,11), determine the slope of the given line (-0.57) and use the point-slope form of the equation to find the equation of the new line, y = -0.57x + 22.4.

Step-by-step explanation:

To find the equation of a line that is parallel to the given line and passes through the point (20,11), we need to determine the slope of the given line. The slope can be found using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Solution:

1. The slope of the given line is calculated as follows:
   
   Slope = (-8 - (-4)) / (17 - (-4)) = -12 / 21 = -0.57
2. Since a line parallel to the given line will have the same slope, the slope of the line we want to find is also -0.57.
3. Using the point-slope form of the equation of a line (y - y1) = m(x - x1), where (x1, y1) is the point (20,11) and m is the slope (-0.57):

y - 11 = -0.57(x - 20)

Simplifying the equation:

y - 11 = -0.57x + 11.4

y = -0.57x + 22.4