Answer:
7. 6x - y = 11
8. x + y = 7
Step-by-step explanation:
The given problem asks for you to write the equations in standard form, Ax + By = C, where A and B ≠ 0, and A is non-negative.
7. Slope = 6; (3, 7)
A good way to start is using the point-slope form, y - y1 = m(x - x1) where m = slope, and (x1, y1) represents the coordinates of the given point.
y - y1 = m(x - x1)
y - 7 = 6(x - 3)
Distribute 6 into the parenthesis:
y - 7 = 6x - 18
Add 7 to both sides:
y - 7 + 7 = 6x - 18 + 7
y = 6x - 11
Subtract 6x from both sides:
- 6x + y = 6x - 6x - 11
-6x + y = -11
Divide both sides by -1 to make the coefficent of x a positive integer:
[tex]\frac{-6x + y}{-1} = \frac{-11}{-1}[/tex]
6x - y = 11 (This is the standard form where A = 6, B = -1, and C = 11).
8. Slope = -1; (2, 5)
Similar to our process in problem #7, substitute the given values into the point-slope form:
y - y1 = m(x - x1)
y - 5 = -1(x - 2)
Distribute 6 into the parenthesis:
y - 5 = -x + 2
Add 5 to both sides:
y - 5 + 5 = -x + 2 + 5
y = -x + 7
Add x to both sides:
x + y = -x + x + 7
x + y = 7 (This is the standard form where A = 1, B = 1, and C = 7).
