Final answer:
To find the equation of a line parallel to 5x + 8y = -7 containing the point (5,2), we rearrange the given line to get the slope, use the point-slope formula, and simplify to y = -(5/8)x + 45/8.
Step-by-step explanation:
To write the equation of a line that is parallel to the line 5x + 8y = -7 and contains the point (5,2), we first need to find the slope of the given line. To do that, we can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The original line equation, when rearranged, becomes y = -(5/8)x - 7/8. This means that the slope of the parallel line must also be -5/8.
Now, using the point-slope form which is y - y1 = m(x - x1), where (x1, y1) is the point the line goes through and m is the slope, we can plug in the slope -5/8 and the point (5,2) to get the equation of the parallel line as y - 2 = -(5/8)(x - 5). Simplifying this, we get the final equation of the line in slope-intercept form, which is y = -(5/8)x + 45/8. This is the equation of the line parallel to 5x + 8y = -7 that passes through the point (5,2).