Question

What is the y-intercept for the equation `7x + 2y = - 12`?

Answer 1

y-intercept = `-6`

Explanation:

Standard form of equation of line is `y=mx+c` , where c is the y-intercept.
So simplify the given equation to match `y=mx+c`

`7x+2y=-12` -----> subtract -7 from both sides
`2y = -12-7x`
`2y=-7x-12`------> rearranging the equation
`y=(-7/2)x - (12/2)` --------> divide by 2 both sides
`y=(-7/2)x - 6` ------> now this is in same format as `y=mx+c`
So the y-intercept is `-6`.

In otherwords, y-intercept is when `x=0`.
this makes:
`7x+2y=-12`
`(7xx0) + 2y= -12`
`0+2y=-12`
`2y=-12`
`y=-12/2`
`y=-6`-----> this is your y-intercept

Answer 2

`y=-6`

Explanation:

`"to find the intercepts, that is where the graph crosses"`
`"the x and y axes"`

`• " let x = 0, in the equation for y-intercept"`

`• " let y = 0, in the equation for x-intercept"`

`x=0rArr0+2y=-12rArry=-6larrcolor(red)"y-intercept"`

`y=0rArr7x+0=-12rArrx=-12/7larrcolor(red)"x-intercept"`
graph{(y+7/2x+6)((x+12/7)^2+(y-0)^2-0.04)((x-0)^2+(y+6)^2-0.04)=0 [-20, 20, -10, 10]}