Final answer:
The equation of the line parallel to 5x + 7y = 13 and passing through the point (-8, 7) is found by using the slope -5/7 from the original line and applying it to the point-slope form with the given point, resulting in y - 7 = -5/7(x + 8).
Step-by-step explanation:
To write the equation of a line parallel to 5x + 7y = 13 and passing through the point (-8, 7), we need to determine the slope of the given line and use it in the point-slope form equation for our new line.
First, rewrite the equation of the given line in slope-intercept form (y = mx + b):
5x + 7y = 13
7y = -5x + 13
y = -⅓x + ⅓⅓
This format shows that the slope of the given line is -⅓. Lines that are parallel have the same slope, so our new line will also have a slope of -⅓.
Next, use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in our point (-8, 7) and the slope -⅓, we get:
y - 7 = -⅓(x + 8)
Finally, simplify this equation if needed to get the desired form, such as slope-intercept form or standard form, depending on instructions or preference.