Write the equation of a line perpendicular to y=1/2x + 8 that passes through ( 4, 9 ).

y = - 2x + 17

Step-by-step explanation:

The equation of a line, represented in the slope-intercept form, is

y = mx + c

Where

Slope = m

c = intercept

Looking at the equation given,

y=1/2x + 8

Slope,m = 1/2

If a line is perpendicular to a another line, then the slope of one line is equal to the negative reciprocal of the other line. It means that the slope of the perpendicular line that passes through that passes through ( 4, 9 ) will be -2

To determine c,

We will substitute m = -2, y = 9 and x = 4 into the slope intercept equation,

y = mx + c. It becomes

9 = -2 × 4 + c

9 = -8 + c

c = 9 + 8 = 17

The equation becomes

y = - 2x + 17

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