Question

What is the slope intercept form of the line with a slope of `-2/3` that passes through `(-5,2)`?

Answer 1

`y=-2/3x-4/3`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`•color(white)(x)y=mx+b`

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

`"here "m=-2/3`

`rArry=-2/3x+blarrcolor(blue)"is the partial equation"`

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

`2=10/3+brArrb=6/3-10/3=-4/3`

`rArry=-2/3x-4/3larrcolor(red)"in slope-intercept form"`

Answer 2

`y= -2/3 x -4/3`

Explanation:

`color(blue)(Slope = m)`

`color(blue)(=> -2/3 = (y-y_1)/(x-x_1))`

Here `color(red)(x_1=-5)`

And `color(red)(y_1=2)`

Put them in the above equation

`color(orange)(=> -2/3 = (y-2)/(x-(-5)))`

`color(orange)(=> -2/3 = (y-2)/(x+5))`

Cross-multiply

`color(purple)(=> -2(x+5)=3(y-2))`

`color(purple)(=> -2x -10=3y-6)`

`color(purple)(=> 6-10=2x+3y)`

`color(green)(=> -4-2x=3y)`

`color(green)(=> 3y=-2x-4)`

`color(green)(=> y=-2/3 x -4/3)`