Find an equation of the line in general form that passes through the point (- 9, 7) and is parallel to the line 8x - 9y - 7 = 0.

Question

Quizplus · Accepted Answer

To find the equation of a line parallel to another line, we use the fact that parallel lines have the same slope.

First, we need to find the slope of the given line. We can rearrange the equation to get it in slope-intercept form (y = mx + b), where m is the slope:

8x - 9y - 7 = 0
-9y = -8x + 7
y = (8/9)x - 7/9

So the slope of the given line is 8/9.

Since the line we're looking for is also parallel, it will have the same slope. We can use the point-slope form of the equation of a line to find the equation:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the common slope.

Plugging in the values we know, we get:

y - 7 = (8/9)(x + 9)

Multiplying both sides by 9 to eliminate the fraction, we get:

9y - 63 = 8x + 72

Now we can rearrange this equation to get it in general form:

8x - 9y + 135 = 0

So the equation of the line we're looking for is 8x - 9y + 135 = 0, which is answer choice D.

Find an Equation of the Line in General Form That