SOLUTION: Write the standard form of an equation of the line that passes through each pair of points: (-5,7), (0,1/2)

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Question 70332This question is from textbook
: Write the standard form of an equation of the line that passes through each pair of points:
(-5,7), (0,1/2)This question is from textbook

Answer by funmath(2925) About Me  (Show Source):
You can put this solution on YOUR website!
Write the standard form of an equation of the line that passes through each pair of points:
(-5,7), (0,1/2)
In order to find the equation of a line, you need a point an a slope. You don't have a slope, but never fear, you have two points and can get the slope using the slope formula:
highlight%28m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29, where m=slope, and (x1,y1) and (x2,y2) are your given points.
(x1,y1)=(-5,7) and (x2,y2)=(0,1/2)
m=%281%2F2-7%29%2F%280-%28-5%29%29
m=%281%2F2-14%2F2%29%2F5
m=%28-13%2F2%29%2F5
m=%28-13%2F2%29%281%2F5%29
m=-13%2F10
Now you have a point and a slope, so you can use the point slope formula to find the equation of the line: highlight%28y-y%5B1%5D=m%28x-x%5B1%5D%29%29, where m=slope and (x1,y1) is a given point.
(x1,y1)=(-5,7) and m=-13/10
y-7=%28-13%2F10%29%28x-%28-5%29%29
y-7=%28-13%2F10%29%28x%2B5%29
The Standard form of a line is highlight%28Ax%2BBy=C%29, where A, B, and C are integers. A lot of books and teachers also require A to be positive.
10%28y-7%29=10%28-13%2F10%29%28x%2B5%29
10y-70=-13%28x%2B5%29
10y-70=-13x-65
13x%2B10y-70=13x-13x-65
13x%2B10y-70%2B70=-65%2B70
highlight%2813x%2B10y=5%29
Happy Calculating!!!