Question

Which equation best represents a line that is perpendicular to the graph? A. y = 1/4x - 1 B. y = -1/4x - 1 C. y = 4x + 4 D. y = -4x - 1

Answer 1

C. y = 4x + 4

Step-by-step explanation

We want to find the line that is perpendicular to the graph.

To do that, we have to find the slope of the graph and find the equation that has a negative inverse slope to the graph.

Note: A linear equation is written generally as:

y = mx + c

where m = slope

The slope of the graph can be found by using formula:

`\text{slope =}(y_2-y_1)/(x_2-x_1)`

where (x1, y1) and (x2, y2) are two points that lie on the graph.

Let us pick the points:

(x1, y1) = (0,1)

(x2, y2) = (4, 0)

The slope of the graph is therefore:

`\begin{gathered} \text{slope = }\frac{\text{0 - 1}}{4\text{ - 0}} \\ \text{slope = -}(1)/(4) \end{gathered}`

The negative inverse of -1/4 is 4.

Therefore, the correct option is Option C because that equation has a slope of 4.