Final answer:
To find the equation of a line perpendicular to 7x - 8y = -9 that passes through (-7,4), we first find the slope of the given line (7/8) then use the negative reciprocal (-8/7) as our slope in the point-slope form, arriving at the final equation y = (-8/7)x - 4.
Step-by-step explanation:
To write the equation of a line perpendicular to the given line 7x - 8y = -9 that passes through the point (-7,4), we first need to find the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope. By rearranging the original equation into slope-intercept form, we get 8y = 7x + 9, and then y = (7/8)x + (9/8). So, the slope of the given line is 7/8. The slope of a line perpendicular to this line will be the negative reciprocal of 7/8, which is -8/7.
Next, using the point-slope form of the equation of a line (y - y1 = m(x - x1)), where m is the slope and (x1,y1) is the point the line passes through, we substitute the slope -8/7 and the point (-7,4). This yields y - 4 = -8/7(x + 7).
To put this in slope-intercept form, y = mx + b, we distribute the slope on the right side: y - 4 = (-8/7)x - 8 and then add 4 to both sides to get y = (-8/7)x - 4.
Therefore, the equation of the line we are looking for is y = (-8/7)x - 4.