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

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ANSWER

f(x) = 1/2x + 2

EXPLANATION

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

[tex]f(x)=mx+b[/tex]

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:

[tex]m=-\frac{1}{n}[/tex]

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

[tex]f(x)=\frac{1}{2}x+b[/tex]

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

[tex]\begin{gathered} 3=\frac{1}{2}\cdot2+b \\ 3=1+b \\ b=3-1 \\ b=2 \end{gathered}[/tex]

The equation is

[tex]f(x)=\frac{1}{2}x+2[/tex]

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