Find an equation of the line passing through each pair of points. Write the equation in the form Ax + By = C.
-(0, -7)and (-5, 1)
A)-8x + 5y = -35
B)7x - 6y = 29
C)8x + 5y = -35
D)-7x + 6y = 29

Question

Quizplus · Accepted Answer

We need to find the equation of the line passing through the points (0, -7) and (-5, 1).

First, we need to find the slope of the line using the formula:
m = (y2 - y1) / (x2 - x1)

m = (1 - (-7)) / (-5 - 0) 
m = 8 / (-5) 
m = -8/5

Now, we use the point-slope form of an equation for a line: 
y - y1 = m(x - x1)

Using the first point (0, -7): 
y - (-7) = (-8/5)(x - 0) 
y + 7 = (-8/5)x

To convert this to the form Ax + By = C, we can multiply both sides by -5: 
-5y - 35 = 8x

Then, rearrange to get the standard form: 
8x + 5y = -35

Therefore, the answer is C. We can use the point-slope formula to find the equation of the line passing through the two given points. 
The formula is: y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is one of the given points. 
First, let's find the slope:
m = (y2 -y1)/(x2 - x1)
m = (1 -(-7))/(-5 - 0) = 8/-5 = -8/5
Next, let's choose one of the given points, say (0, -7), and substitute its coordinates along with the slope into the point-slope formula:
y - (-7) = (-8/5)(x - 0)
Simplifying and putting the equation in the form Ax + By = C:
y + 7 = (-8/5)x
8x + 5y + 35 = 0
Multiplying all terms by -1 to get the desired form:
-8x - 5y + 35 = 0
8x + 5y = 35
Therefore, the equation of the line passing through the given points is 8x + 5y = 35. So, the best choice is C.

Find an Equation of the Line Passing Through Each Pair