Question

Which equations represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2)?

A.) y = -3/4x + 1
B.) 3x - 4y = -4
C.) 4x - 3y = -3
D.) y - 2 = -3/4 (x - 4)
E.) y + 2 = 3/4 (x + 4)

Answer 1

The equation that represents the line parallel to 3x - 4y = 7 and passing through the point (-4, -2) is E.) y + 2 = 3/4 (x + 4), following the point-slope form for a parallel line with the same slope of 3/4.

Step-by-step explanation:

The question asks which equations represent a line that is parallel to the line given by the equation 3x - 4y = 7 and which also passes through the point (-4, -2). To determine which equations meet these criteria, we first need to find the slope of the given line. By converting the equation into slope-intercept form (y = mx + b), where 'm' represents the slope, we find that the slope of the given line is 3/4. A parallel line would have the same slope. We then use the point-slope form of the equation for a line, which is (y - y1) = m(x - x1), where (x1, y1) is a point on the line and 'm' is the slope. Substituting the slope and the point (-4, -2) into this equation, we get:

y + 2 = 3/4(x + 4)

This corresponds to option E.) y + 2 = 3/4 (x + 4). Therefore, option E is the correct equation that meets the specified conditions.