Find the equation of the line parallel to the graph of 4 x - y = 5 that contains the point (- 3, 1).

Question

Quizplus · Accepted Answer

To find the equation of a line parallel to a given line, we need to use the fact that parallel lines have the same slope. We can rewrite the given equation 4x - y = 5 in slope-intercept form (y = mx + b) by solving for y:

4x - y = 5

-y = -4x + 5

y = 4x - 5

So, the slope of the given line is 4.

Since the parallel line we're looking for also has a slope of 4, we can start the equation in point-slope form:

y - y1 = m(x - x1), where (x1, y1) is the point (-3, 1).

Plugging in m = 4, x1 = -3, and y1 = 1, we get:

y - 1 = 4(x + 3)

Now we can simplify to slope-intercept form:

y = 4x + 13

So, the equation of the line parallel to 4x - y = 5 that contains the point (-3, 1) is y = 4x + 13 and the correct choice is C.

Find the Equation of the Line Parallel to the Graph