Question

i need help understanding what to do. my summer school teacher told me to go to this website but i can’t use it if i don’t know what to do, can you help me please?

Answer 1

Remember that for two equations to be perpendicular, their slopes must be the negative reciprocal of each other.

In the given equation, y = -2x + 18, the slope is -2.

Therefore, the slope of the line perpendicular to this equation must be 1/2.

So, now we have slope = 1/2 and a point at (-4, 12).

Let's determine the equation using the slope-point formula.

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

where m = slope and (x₁, y₁) = the coordinate of the given point.

Let's replace the variables in the formula with their corresponding numerical values. m = 1/2, x₁ = -4, y₁ = 12

`y-12=(1)/(2)(x-(-4))`

Then, simplify.

`y-12=(1)/(2)(x+4)`

Multiply 1/2 by the terms inside the parenthesis.

`y-12=(1)/(2)x+2`

Add 12 on both sides of the equation.

`y-12+12=(1)/(2)x+2+12`
`y=(1)/(2)x+14`

Hence, the equation of the line perpendicular to y = -2x + 18 and passes through the point (-4, 12) is y = 1/2x + 14 as shown above.

See the graph below: