Answer:
c) -2y = 10x + 6
Step-by-step explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]
The variables stand for:
[tex]y:$ y-coordinate of any point on the line\\$x:$ x-coordinate of any point on the lien\\$m: $ Slope of the line\\$b: $ y-intercept of the line; where the line meets the y-axis[/tex]
Plugging in the given information into the equation:
[tex]y=-5x+(-3)\\y=-5x-3[/tex]
Go through the answer choices:
a) 2y = -5x - 3
Divide both sides of the equation by 2
[tex]y=-\frac{5}{2}x-\frac{3}{2}\rightarrow\text{Incorrect!}[/tex]
b) -2y = 10x - 6
Divide both sides of the equation by -2
[tex]y=\frac{10}{-2}x-\frac{6}{-2}\\y=-5x-(-3)\\y=-5x+3\rightarrow\text{Incorrect!}[/tex]
c) -2y = 10x + 6
Divide both sides of the equation by -2
[tex]y=\frac{10}{-2}x+\frac{6}{-2}\\y=-5x+(-3)\\y=-5x-3\rightarrow\text{Correct!}[/tex]
d) 2y = 10x - 6
Divide both sides of the equation by 2
[tex]y=\frac{10}{2}x-\frac{6}{2}\\y=5x-3\rightarrow\text{Incorrect!}[/tex]
Therefore the answer is c) -2y = 10x + 6
Additional Comments:
We can only divide both sides of the equation by 2 and/or -2 because of the Division Property of Equality. This property states that if we divide one side of the equation by a certain quantity, we must divide the other side by the same quantity so that the equation remains equal.
