a line passes through the points (-3,-4) and (2,8). write an equation that represents a line parallel to this line passing through the point (-2,5).

Answer 1

There are two features in the question to help you decide the approach; they are "line" and "parallel". Because it is a line, it will have a "slope"; and, because the lines are parallel, they will have the same slope. Therefore, 1. Find the slope of the known line (-3,-4) and (2,8), next 2. Assign that slope to the second line and then 3. use the slope and the point (-2,5) on the second (parallel) line to determine the second point on the unknown parallel line. Put simply: get the slope of the first line, which is the slope of the second line, then find the missing point for the second line.

1. Get the slope: slope = (y2-y1)/(x2-x1) = (8-(-4))/(2-(-3)) = 12/5
2. Set the slope equal to the unknown line having point (-2,5): (y2-y1)/(x2-x1)=(y2-5)/(x2-(-2) = 12/5
3. Solve both equations: y2 - 5 = 12, y2 = 18 and x2 + 2 = 5, x2 = 3 therefore the point is (3,18)

So the parallel line is (-2,5) (3,18). If you graph it, you will see it is parallel to (-3,-4) (2,8). I hope the helps.

Answer 2

I'll assume the "slope-intercept form: y = mx + b. m is the slope and b is the y intercept (where x = 0)

First get the slope for the given line: The slope is (y1 - y2)/(x1 - x2)

plugging in the numbers, we get:

(-4 - 8)/(-3 - 2) = 12/5

for a parallel line, we need the same slope, so m in the new equation is 12/5

Next, plug in the given x and y values (from the point (-2,5) and solve for b:

5 = 12/5 * (-2) + b

b = 5 + 24/5 = 49/5 = 9.8

CHECK by plotting both lines on graph paper or with a plotting tool