Question

Which is the equation of a line that has a slope of -5 and a y-intercept of -3? Show me how you arrived at your answer.

a) 2y = -5x - 3
b) -2y = 10x - 6
c) -2y = 10x + 6
d) 2y = 10x - 6 ​

Answer 1

c) -2y = 10x + 6

Explanation:

The equation of a line in slope-intercept form is:

`y=mx+b`

The variables stand for:

`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`

Plugging in the given information into the equation:

`y=-5x+(-3)\\y=-5x-3`

Go through the answer choices:

a) 2y = -5x - 3

Divide both sides of the equation by 2

`y=-(5)/(2)x-(3)/(2)\rightarrow\text{Incorrect!}`

b) -2y = 10x - 6

Divide both sides of the equation by -2

`y=(10)/(-2)x-(6)/(-2)\\y=-5x-(-3)\\y=-5x+3\rightarrow\text{Incorrect!}`

c) -2y = 10x + 6

Divide both sides of the equation by -2

`y=(10)/(-2)x+(6)/(-2)\\y=-5x+(-3)\\y=-5x-3\rightarrow\text{Correct!}`

d) 2y = 10x - 6

Divide both sides of the equation by 2

`y=(10)/(2)x-(6)/(2)\\y=5x-3\rightarrow\text{Incorrect!}`

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.