Question

A given line has the equation 10x+2y=−2 . What is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y=−5x+12 5x+y=12 y−12=5(x−0) 5x+y=−1

Answer 1

Answer:
`y=-5x+12` or
`5x+y=12`

Explanation:

The given equation of a line:
`10x+2y=-2`

Rewrite equation of line in slope intercept form (y=mx+c) by subtracting 10 on both sides and then divide both sides by 2, we get

`y=-5x-1`

Slope of line : m= -5 [Coefficient of x]

Since , the slope of two parallel lines are equal.

Then, slope of line parallel to given line= -5

Equation of a line passing through point (a,b) and has slope p is given by :-

`(y-b)=p(x-a)`

Similarly, Equation of a line passing through point (0,12) and has slope -5 is given by :-

`(y-12)=(-5)(x-0)\\\\\Rightarrow\ y-12=-5x\\\\\Rightarrow\ 5x+y=12`

Answer 2

y = -5x + 12

Explanation:

10x + 2y = −2

-10x - 10x

_______________

2y = -10x - 2

__ ________

2 2

y = -5x - 1, [0, 12] ∥↷

12 = -5[0] + b

0

12 = b

y = -5x + 12

I am joyous to assist you anytime.