Question

find the equation of the line passing through (2,3) and perpendicular to the line y=-2×+5. Write the equation in function notation

Answer 1

f(x) = 1/2x + 2

Step-by-step explanation

The equation for a line with slope m and y-intercept b is:

`f(x)=mx+b`

If a line is perpendicular to another line with slope n, the slope of the line we want to find is the reciprocal and opposite:

`m=-(1)/(n)`

In this case, n = -2, so the slope of our line is m = 1/2:

`f(x)=(1)/(2)x+b`

To find b we use the point: f(2) = 3:

`\begin{gathered} 3=(1)/(2)\cdot2+b \\ 3=1+b \\ b=3-1 \\ b=2 \end{gathered}`

The equation is

`f(x)=(1)/(2)x+2`