Question

Someone please help me with this! Thanks :)

Answer 1

`y=2x+7`

Explanation:

Given the equation

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

comparing the equation with the slope-intercept form

`y=mx+b`

Here,

• m is the slope

• y is the intercept

so the slope of the line is -1/2

As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so

the slope of the perpendicular line will be: 2

Therefore, the point-slope form of the equation of the perpendicular line that goes through (-2, 3) is:

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

substituting the values m = 2 and the point (-2, 3)

`y-3=2\left(x-\left(-2\right)\right)`

`y-3=2\left(x+2\right)`

Add 3 to both sides

`y-3+3=2\left(x+2\right)+3`

`y=2x+7`