Question

Write the equation of the line

through the given points or described below.

1.- (-3, 7) and (6, -5)



2.- A line parallel to y = 2x - 5 and goes through (1, 2)



3.- A line perpendicular to
y = -8x + 75 and goes through (-16, 5)

Answer 1

To find the equation of the line passing through (-3, 7) and (6, -5), use the formula for slope and the formula for the y-intercept.

Step-by-step explanation:

To find the equation of the line passing through the points (-3, 7) and (6, -5), we need to determine the slope and the y-intercept of the line.

Step 1: Calculate the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)

m = (-5 - 7) / (6 - (-3))
m = (-12) / (9)
m = -4/3

Step 2: Use the slope and one of the given points to find the y-intercept (b) using the formula:
y = mx + b

Using the point (-3, 7):
7 = (-4/3)(-3) + b

b = 7 - (4) + 3
b = -8

Step 3: Write the equation in slope-intercept form:
y = mx + b

y = (-4/3)x - 8