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

♪ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ♪

`\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{$\displaystyle(y_2-y_1)/(x_2-x_1)$}`

our values are:

• (-2, 10) and (4, -8)

after substituting the values into the above formula, we obtain

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

after simplifying, we obtain

`\large\text{$\displaystyle(-18)/(4+2)$}`

simplifying more,

`\large\text{$\displaystyle(-18)/(6)$}`

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!}`