Find an equation for the line with the given properties. Write the equation in slope-intercept form, if possible.
-Parallel to the line 9x + 7y = 126; containing the point (7, 17)
A) 7x + 9y = 17
B) 9x + 7y = 182
C) 9x - 7y = 182
D) 7x + 7y = 126

Question

Quizplus · Accepted Answer

Lines that are parallel have the same slope. The given line can be rewritten in slope-intercept form (y = mx + b) to find its slope. Starting with 9x + 7y = 126, we subtract 9x from both sides to get 7y = -9x + 126, then divide by 7 to isolate y, resulting in y = -9/7x + 18. This shows the slope is -9/7. A line parallel to this must have the same slope. To find the specific line that goes through the point (7, 17), we use the point-slope form y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point. Substituting the given point and slope, we get y - 17 = -9/7( x - 7). Simplifying this equation to get it back into the form of 9x + 7y = C, where C is a constant, will give us the equation of the line parallel to the given line and passing through (7, 17). When we do the math, we find that the correct equation is 9x + 7y = 182, which matches option B.

Find an Equation for the Line with the Given Properties