Question

Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form. (x, y) = (−2, 10) and (x, y) = (4, −8) are points on the line

Answer 1

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$\textsc{heya!}$

☑︎  what we need to do:

• find the equation of the line

☑︎ what we are provided with:

• two points on this line

$\textsc{solution:}$

• equation: y=-3x+4

$\textsc{explanation:}$

first, these are the points on our line:

• (-2, 10) • (4, -8)

what we need at this moment is the gradient (slope) of the line.

remember, there's a little formula that will help us find the gradient:

$\large\text{ \displaystyle\frac{y_2-y_1}{x_2-x_1} }$

our values are:

• (-2, 10) and (4, -8)

after substituting the values into the above formula, we obtain

$\large\text{ \displaystyle\frac{-8-10}{4-(-2)} }$

after simplifying, we obtain

$\large\text{ \displaystyle\frac{-18}{4+2} }$

simplifying more,

$\large\text{ \displaystyle\frac{-18}{6} }$

dividing,

$\large\text{ -3 }$

but that's only part of our problem. we need to find the equation, and we have the gradient only.

let's use the first point in our equation

• (-2, 10)

• $\large\text{ y-y_1=m(x-x_1) }$

m is the gradient.

this is what we obtain after substituting the values

$\large\text{ y-10=-3(x-(-2) }$

simplifying

$\large\text{ y-10=-3(x+2) }$

simplifying more

$\large\text{ y-10=-3x-6 }$

moving 10 to the right side

$\large\text{ y=-3x-6+10 }$

and finally

$\large\text{ y=-3x+4 }$

$\textsc{hopefully\:helpful}$

by:    • $\textsc{ d^an_ci^ng }$

$\textsc{have\:a\:great\:rest\:of\:your\:day\:ahead!}$