Question

A line contains (-3,19) and (1,18). which equation represents the line that is parallel to the given line and passes through point (-4, -9)?

A.) y = 1/4x - 8
B.) y = 1/4x - 10
C.) y = -1/4x - 8
D.) y = -1/4x - 10

Answer 1

The equation of the line that is parallel to the given line with points (-3,19) and (1,18), and passes through the point (-4, -9) is y = -1/4x - 10.

Step-by-step explanation:

To find the equation of a line that is parallel to the given line and passes through a specific point, we first need the slope of the original line. We can calculate the slope using the two points given: (-3,19) and (1,18). The formula for slope, m, is (y2 - y1) / (x2 - x1). Applying this to the points:

m = (18 - 19) / (1 - (-3))

m = -1 / 4

The slope of the parallel line must be the same, so the slope is also -1/4. Now, we use the point-slope form of the equation, y - y1 = m(x - x1), where (x1, y1) is the point (-4, -9), and m is -1/4:

y - (-9) = -1/4(x - (-4))

y + 9 = -1/4x - 1

y = -1/4x - 10

Therefore, the equation of the line parallel to the original one and passing through (-4, -9) is y = -1/4x - 10.