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

ANSWER

f(x) = 1/2x + 2

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:

$m=-\frac{1}{n}$

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

$f(x)=\frac{1}{2}x+b$

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

$\begin{gathered} 3=\frac{1}{2}\cdot2+b \\ 3=1+b \\ b=3-1 \\ b=2 \end{gathered}$

The equation is

$f(x)=\frac{1}{2}x+2$