Question

What is the equation in point-slope form and slope intercept form for the line given slope= 8/3,(-2,-6)?

Answer 1

Answer:

Step-by-step explanation:

y = 8x/3 - 2/3.

Answer 2

The equation in point-slope form is

$(y+6)=\frac{8}{3}(x+2)$

Equation in slope intercept form is

$y=\frac{8}{3}x-\frac{2}{3}$

Step-by-step explanation:

Given slope of the line

$m=\frac{8}{3}$

The line passes through the point (-2, -6)

We know that equation of a line with slope m and passing through point $(x_1,y_1)$ is given by

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

Therefore, the equation of the line is

$(y-(-6))=\frac{8}{3}(x-(-2))$

$\implies (y+6)=\frac{8}{3}(x+2)$

$\implies 3(y+6)=8(x+2)$

$\implies 3y+18=8x+16$

$\implies 8x-3y=2$

This is the equation of the line

Equation of the line in slope intercept form

We can write the above equation as

$3y=8x-2$

$\implies y=\frac{8}{3}x-\frac{2}{3}$

Comparing this equation with the general equation of the slope intercept form i.e. $y=mx+c$

We get

$m=\frac{8}{3}$

And $c=\frac{2}{3}$

Hope this answer is helpful.

Know More:

Q: Reduce the following equation into slope intercept form and find their slope and y- intercept

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