What is the equation of a line that passes through the point (1, 8) and is perpendicular to the line whose equation is y=x/2+3 ?

Mathematics

1 answer:

Svet_ta [14]3 years ago

3 0

<u>Answer</u>

y = -2x + 10

<u>Explanation</u>

The general equation for a straight line is y = mx + c where m and c are gradient and y-intercept respectively.

y=x/2+3 = y (1/2)x + 3

gradient = 1/2

Gradient of the line perpendicular to y=x/2+3 is;

m × 1/2 = -1

m = -2

Now we find the equation of a line passing through (1,8) and have a gradient of -2.

-2 = (y - 8)/(x - 1)

-2(x - 1) = (y - 8)

2 -2x = y - 8

y = -2x + 10

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ElenaW [278]

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Next, we need to figure out which side to shade. To do so, simply pick any point (I like to use the point (0,0) because it makes the calculations easy) and see whether it satisfies the inequality. If it does, shade the side with that point, and if not, shade the opposite side of the graph.

Here we see that the point (0,0) does satisfy the inequality, since -(0) + 4(0) is 0, and 0 ≥ -8, so the top half of the graph should be shaded (see the second image).