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Rudiy27
3 years ago
14

Find the equation of the straight line through (–2, 3) perpendicular to 2x + y =8

Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
8 0

Answer:

y = \dfrac{1}{2}x + 4

Step-by-step explanation:

The equation of a line in slope-intercept form is

y = mx + b

We need to find the slope, m, and the y-intercept, b.

The line we need is perpendicular to the line 2x + y = 8.

<em>The slopes of perpendicular lines are negative reciprocals.</em>

We solve the given equation for y to find the slope of the given line.

2x + y = 8

y = -2x + 8

The given line has slope -2.

The negative reciprocal of -2 is 1/2.

Our line has slope, m = 1/2.

Now we have

y = 1/2 x + b

Now we use the given point, (-2, 3), for x and y, using x = -2, and y = 3, and we solve for b.

y = 1/2 x + b

3 = 1/2 * (-2) + b

3 = -1 + b

4 = b

b = 4

Now we have

y = 1/2 x + 4

Answer: y = \dfrac{1}{2}x + 4

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