Question

Write an equation in point-slope form of the line that passes though the given points. Then, write the equation in slope intercept form.

(-1,-2) and (2,4)

Answer 1

Please check the explanation.

Explanation:

Given the points

• (-1, -2)

• (2, 4)

Finding the slope between (-1, -2) and (2, 4)

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(2,\:4\right)`

`m=(4-\left(-2\right))/(2-\left(-1\right))`

`m=2`

Using the point-slope form

`y-y_1=m\left(x-x_1\right)`

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 2 and the point (-1, -2)

`y-y_1=m\left(x-x_1\right)`

`y -(-2) = 2(x-(-1)`

Thus, the point-slope form of the line equation is

`y -(-2) = 2(x-(-1)`

now, write the slope-intercept form of the line equation y = mx+b

`y-\left(-2\right)=2\left(x-\left(-1\right)\right)`

`y+2=2\left(x+1\right)`

subtract 2 from both sides

`y+2-2=2\left(x+1\right)-2`

Simplify

`y=2x+0`

`y = 2x`

Therefore, the equation in slope-intercept form is:

• 
  `y = 2x`