Question

What is the equation of the line in point-slope form that passes through the point (-6, 7) and is parallel to the line 4x−6y=18?

A. y−7=32(x+6)
B. y−7=−32(x+6)
C. y+7=32(x−6)
D. y+7=−32(x−6)

Answer 1

The equation of the line in point-slope form that passes through the point (-6, 7) and is parallel to the line 4x−6y=18 is y - 7 = (2/3)(x + 6).

Step-by-step explanation:

To find the equation of the line in point-slope form that is parallel to the line 4x−6y=18, we need to find the slope of the given line. The equation of a line in point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

First, we need to rearrange the given line equation to slope-intercept form (y = mx + b). 4x - 6y = 18 can be rewritten as -6y = -4x + 18, and then as y = (2/3)x - 3. So the slope of the given line is 2/3.

Since we want a line that is parallel, it will have the same slope. So, the equation of the line in point-slope form that passes through the point (-6, 7) and is parallel to the line 4x−6y=18 is y - 7 = (2/3)(x + 6). Therefore, the correct option is A. y-7= (2/3)(x+6).