Question

Question #bccac

Answer 1

By converting the equation in point-slope form to slope-intercept form, we obtain `y=\frac{8}{9}x+\frac{8}{3}`

Explanation:

Given the slope of a line and a point on it, we can write its equation in point-slope form, denoted by:

`y-y_1=m(x-x_1)`

Where `m` is the slope, and `(x_1,y_1)` is a point on the line.

Let’s plug those values in:

`y-(-8)=\frac{8}{9}(x-6)`

`\implies y+8=\frac{8}{9}(x-6)`

We can now move around terms to convert this to slope-intercept form:

`y=8=\frac{8}{9}(x-6)`

`\implies y+8=\frac{8}{9}x-\frac{16}{3}`

`\implies y=\frac{8}{9}x+\frac{8}{3}`

Answer 2

`y=8/9x-40/3`

Explanation:

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`

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

`"here "m=8/9`

`rArry=8/9x+blarrcolor(blue)"is the partial equation"`

`"to find b substitute "(6,-8)" into the partial equation"`

`-8=(8/9xx6)+brArrb=-8-16/3=-40/3`

`rArry=8/9x-40/3larrcolor(red)"in slope-interceot form"`