Question

What is the equation of a line through `(-1,-2)` and is parallel to `y=7x-3`?

Answer 1

`y=7x+5`

Explanation:

The equation of a st line parallel to `y=7x-3` is `y=7x+c`
Again it passes through `(-1,-2)`
So `-2=7(-1)+c =>c=7-2=5`
Hence the required equation is `y=7x+5`

Answer 2

The equation of the line is `y=7x+5`

Explanation:

The slope of the line `y=7x-3` is 7 ; which is also the slope of any line parallel to it. The equation of the line passing through `(-1,-2)` is `y+2=m(x+1)or y+2 = 7(x+1)` or `y=7x+5` [Ans]

Answer 3

The graph line parallel to `color(brown)(y=7x-3)" "is" "color(green)(y=7x+5)`

Explanation:

Standard equation form `y=mx+c`

Where m is the gradient

Note that the gradient is the amount of up or down for the amount of along. Think about the incline of a hill.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Solving your question")`

Given;`" "color(brown)(y=7x-3)`

the coefficient of `x` is 7. This is the gradient. So a parallel plot will have the same gradient. If it did not then they would cross at some point.

So `color(brown)(y=mx+c)" becomes "color(green)(y=7x+c)`

We are told that it passes through the point `(x,y)->(-1,-2)`

So by substitution we have

`" "color(green)(y=7x+c" "->" "(-2)=7(-1)+c`

`" "color(green)(-2=-7+c)`

Add `color(red)(7)` to both sides

`color(green)(-2color(red)(+7)=-7color(red)(+7)+c`

`" "color(green)(5=0+c)`

`c = +5`

So `color(brown)(y=mx+c)" becomes "color(green)(y=7x+5)`