Question

Write the equation of the line that is perpendicular to the line given and through the given point. Do not use spaces in your equation. y=-2X+1 (0,5) *

Answer 1

y = 0.5x + 5

Step-by-step explanation:

The equation of a line can be calculated as:

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

Where m is the slope and (x1, y1) is a point in the line.

To find the slope of our line, we need to identify the slope of the given line.

Since the equation of the given line is y = -2x + 1, the slope of this line is -2, because it is the number beside the x.

Then, two lines are perpendicular if the product of their slopes is equal to -1. So, we can write the following equation:

`-2\cdot m=-1`

Therefore, the slope m of our line will be:

`m=(-1)/(-2)=0.5`

Now, we can replace the value f m by 0.5 and the point (x1, y1) by (0, 5) and we get that the equation of the line is:

`\begin{gathered} y=0.5(x-0)+5 \\ y=0.5(x)+5 \\ y=0.5x+5 \end{gathered}`

Therefore, the answer is y = 0.5x + 5