Question

How do you write the standard form of the equation given (-2,5) and slope -4?

Answer 1

`y = -4x-3`

Explanation:

The given values of `(-2,5)` and `-4` represent `x,y and m` in
`y=mx+c`, which is the equation of a straight line.

Substitute these values to find the value of `c`, the `y`-intercept.

`y= mx+c`

`5 = (-4)(-2) +c`

`5 = 8+c`

`5-8=c`

`-3=c`

The required equation is:

`y = -4x-3`

Answer 2

`4x+y=-3`

Explanation:

`"the standard form of the equation of a line is"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))`
where A is a positive integer and B, C are integers.

`"we can establish the equation in "color(blue)"slope-intercept form"`

`•color(white)(x)y=mx+b`

`"where m is the slope and b the y-intercept"`

`"here "m=-4`

`rArry=4x+blarr" partial equation"`

`"to find b substitute "(-2,5)" into the equation"`

`5=8+brArrb=-3`

`rArry=-4x-3larrcolor(red)" in slope-intercept form"`

`rArr4x+y=-3larrcolor(red)" in standard form"`