Question

How do you find the general form of the line with slope -2 passing through the point (-4, 6)?

Answer 1

`y=-2x+c` is the general equation with a slope of -2

Now put (-4,6) into the equation to find the specific equation

`6=-2xx-4+c`

`6=8+c`

`-2=c`

`=> y=-2x-2`

Answer 2

`2x+y+2=0`

Explanation:

`"the equation of a line in "color(blue)"general form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By+C=0)color(white)(2/2)|)))`

`"where A is a positive integer and B, C are integers"`

`"obtain 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=-2`

`y=-2x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(-4,6)" into the partial equation"`

`6=8+brArrb=6-8=-2`

`y=-2x-2larrcolor(red)"in slope-intercept form"`

`"subtract "2x-2" from both sides"`

`2x+y+2=0larrcolor(red)"in standard form"`

Answer 3

`y=-2x-2`

Explanation:

Slope is always -2 which means it is a straight line where `y` increases by -2 for every 1 that `x` increases.

i.e. `y` decreases by 2 for every 1 that `x` increases.

The general form will therefore be:

y=-2x +c (where `c` is a constant that we don't know yet).

To find `c` we need to know where the line crosses the Y axis
(when `x=0` then `y=-2(0)+c`, i.e. `y=c`)

The point (-4, 6) tells us that when `x` is -4, `y` is 6, so using these 2 values in the general form equation:
`6=-2(-4)+c`
`6=8+c`
`6-8=c`
c=-2

so the equation for the line is y=-2x-2

check this by putting x=-4 into the equation and seeing if y = 6:
y = -2(-4) - 2 = 8 - 2 = 6 (looks correct)