Find an equation of the line passing through each pair of points. Write the equation in the form Ax + By = C.
-(-6, 2)and (-1, 5)
A)-3x - 5y = -28
B)8x + 6y = -38
C)3x - 5y = -28
D)-8x - 6y = -38

Question

Quizplus · Accepted Answer

To find the equation of a line, we need to use the slope-intercept form or point-slope form. We can use the point-slope form:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the given points. To find the slope, we can use the slope formula:

m = (y2 - y1)/(x2 - x1)

where (x2, y2) is the other given point. Substituting the given points, we have:

m = (5 - 2)/(-1 - (-6)) = 3/5

Then using the point-slope form with the point (-1, 5), we have:

y - 5 = 3/5(x - (-1))

Multiplying both sides by 5 to get rid of the fraction, we obtain:

5y - 25 = 3x + 3

Rearranging terms and putting the equation in the form Ax + By = C, we have:

3x - 5y = -28

Therefore, the answer is choice letter C. Using point-slope form: 
slope = (change in y) / (change in x) = (5-2)/(-1-(-6)) = 3/5
Choose one point (-6, 2) and plug it in to get:
y - 2 = (3/5)(x + 6)
Simplify to get:
5y - 10 = 3x + 18
3x - 5y = -28
which is the equation in the form Ax + By = C.

Find an Equation of the Line Passing Through Each Pair