What is an equation of the line?

What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x − y = 4?

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Find the slope of the given line.

​2x - y = 4
-y = -2x + 4 {subtracted 2x from each side}
y = 2x - 4 {divided each side by -1}

slope of given line is 2

Perpendicular lines have slopes which are negative reciprocals.

slope of new line is -1/2

Substitute the point and slope into slope-intercept form.
slope is -1/2 and the point is (4,1)

y = mx + b {slope-intercept form}
1 = (-1/2)(4) + b {substituted into slope-intercept form}
1 = -2 + b {multiplied -1/2 by 4}
b = 3 {added 2 to each side}

y-intercept is 3

Substitute slope and y-intercept into slope-intercept form.

y = (-1/2) x + 3 is the equation of the line

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