Question

How do you graph using the intercepts for -4x-2y=14#?

Answer 1

See explanation

Explanation:

This is a straight line equation.

`color(blue)("Using first principles method")`

Given:`" "-4x-2y=14`

Add `2y` to both sides

`14+2y=-4x`

Subtract 14 from both sides

`2y=-4x-14`

Divide both sides by 2

`y=-4/2x-14/2`

`color(blue)(y=-2x-7)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("Using shortcut method")`
`color(brown)("It takes a lot more lines to explain than to do it!")`

Move `-2y` to the other side of = and change its sign
`-4x=14+2y`

Move the 14 to the other side of = and change its sign

`-4x-14=2y`

Write as:
`2y=-4x-14`

Move the 2 from `2y` to the other side of the = and change it from multiply to divide (reverse its action)
`y=-4/2 x-14/2`

`color(blue)(y=-2x-7)`..................Equation(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The intercepts are at when `x=0` and `y=0`

`color(brown)("Set "x=0" so Equation(1) becomes:")`

`y=-2(0)-7`
`y=-7 ->" "color(blue)((x,y)=(0,-7) larr" y-intercept")`

`color(brown)("Set "y=0" so Equation(1) becomes:")`

`0=-2x-7`

`+2x=-7`

`x=-7/2->" "color(blue)((x,y)=(-7/2,0)larr" x-intercept")`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mark your two points and draw a straight line through them