8. What is the equation of the line that contains (2, 3) and is perpendicular to the line y = 2x + 3? A.) y = 4x + 2
B.) y= -1/2 x 4
C.) y = -1/2 x +4 D.) y= -4x - 2 E.) none of these

Hi there! :)

Given equation:

y = 2x + 3

A perpendicular line would have a slope of the negative reciprocal, therefore:

2x --> -1/2x

Use the equation y = mx + b to plug in the given point values along with the slope to solve for the final equation:

3 = -1/2(2) + b

3 = -1 + b

3 + 1 = b

b = 4

Therefore, the final equation is:

y = -1/2x + 4

The correct answer choice is C, y = -1/2x + 4.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2