Find an equation of the line passing through each pair of points. Write the equation in the form Ax + By = C.
-(5, 8)and (0, -5)
A)13x + 5y = -25
B)-3x + 5y = -25
C)-13x + 5y = -25
D)3x - 5y = -25

Question

Quizplus · Accepted Answer

Using the slope-intercept form, we can find the slope of the line passing through (5, 8) and (0, -5):
m = (y2 - y1) / (x2 - x1) = (-5 - 8) / (0 - 5) = 13/5
Then, we can use the point-slope form with either point to get the equation in slope-intercept form:
y - 8 = (13/5)(x - 5)
y = (13/5)x - 13 + 8
y = (13/5)x - 5
Finally, we convert to the standard form Ax + By = C by multiplying both sides by 5 and rearranging terms:
-13x + 5y = -25 Using the two-point form formula, we can find the slope of the line:

slope = (y2 - y1)/(x2 - x1) = (-5 - 8)/(0 - 5) = -13/5

Now we can use the point-slope form to find the equation:

y - y1 = m(x - x1)
y - 8 = (-13/5)(x - 5)   [using (5,8) as a point]
y - 8 = (-13/5)x + 13
13x - 5y = -25         [rewriting in the form Ax + By = C]

Therefore, the correct choice is C.

Find an Equation of the Line Passing Through Each Pair