Question

Which of the following equations represents a line that is parallel to

y=−4x−1 and passes through the point (2, 2)?
Options:
A. 4x−6
B. y=−1/4 x+2
C. y=−4x+10
D. y=−4x+4

Answer 1

The equation that represents a line parallel to y = -4x - 1 and passes through the point (2, 2) is y = -4x + 10.

Step-by-step explanation:

To find a line that is parallel to y = -4x - 1 and passes through the point (2, 2), we need to find an equation with the same slope as -4. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.

In the equation y = -4x - 1, the slope is -4.

To find a line that is parallel, we need to keep the same slope. So the equation will be of the form y = -4x + b. To find the y-intercept, we substitute the coordinates of the given point (2, 2) into the equation: 2 = -4(2) + b. Solving this equation gives us b = 10.

Therefore, the equation that represents a line parallel to y = -4x - 1 and passes through the point (2, 2) is y = -4x + 10, which is option C.