Question

Which of the following statements is true about the equation of a line that is parallel to 3x - 4y = 7 and passes through the point (-4,2)?

A) 3x - 4y = 2
B) 3x - 4y = -4
C) 4x - 3y = 14
D) 4x - 3y = -8
E) 4x - 3y = -10

Answer 1

To find the equation of a line parallel to 3x - 4y = 7 and passing through (-4,2), we need to find the slope of the given line and use it to write the equation in slope-intercept form. The equation of the desired line is y = (3/4)x + 5/2.

Step-by-step explanation:

To determine the equation of a line that is parallel to 3x - 4y = 7 and passes through the point (-4,2), we need to find the slope of the given line and use it to write the equation in slope-intercept form.

The given equation can be rewritten as y = (3/4)x - 7/4.

Since parallel lines have the same slope, the slope of the desired line is also 3/4.

Using the coordinates of the given point, we can write the equation as y = (3/4)x + b, where b is the y-intercept. Plugging in the coordinates (-4,2), we get 2 = (3/4)(-4) + b.

Solving for b, we find that b = 5/2. Therefore, the equation of the line parallel to 3x - 4y = 7 and passing through (-4,2) is y = (3/4)x + 5/2.