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Find the equation for the line that passes through the point (5,−5), and that is perpendicular to the line with the equation x+2y=−8.

User GrahamS
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Answer:

The equation of the line passing through the point (5, -5) and perpendicular to the line x + 2y = -8 is y = 2x - 15.

Explanation:

To find the equation of the line passing through the point (5, -5) and perpendicular to the line x + 2y = -8, we need to follow these steps:

Step 1: Convert the given equation into slope-intercept form

Step 2: Find the slope of the given line

Step 3: Find the slope of the line perpendicular to the given line

Step 4: Use the point-slope form to find the equation of the line passing through (5, -5) with the perpendicular slope

Step 1: Convert the given equation into slope-intercept form

To convert x + 2y = -8 into slope-intercept form (y = mx + b), we need to isolate y on one side of the equation:

x + 2y = -8

2y = -x - 8

y = (-1/2)x - 4

So the slope-intercept form of the given equation is y = (-1/2)x - 4, where the slope (m) is -1/2 and the y-intercept (b) is -4.

Step 2: Find the slope of the given line

From the slope-intercept form of the given equation, we can see that the slope (m) is -1/2.

Step 3: Find the slope of the line perpendicular to the given line

The slope of a line perpendicular to another line is the negative reciprocal of its slope. So the slope of the line perpendicular to the given line is the negative reciprocal of -1/2, which is 2.

Step 4: Use the point-slope form to find the equation of the line passing through (5, -5) with the perpendicular slope

We now have the slope (m = 2) and the point (5, -5) through which the line passes. We can use the point-slope form of a line to find its equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Substituting the values, we get:

y - (-5) = 2(x - 5)

y + 5 = 2x - 10

y = 2x - 15

So the equation of the line passing through the point (5, -5) and perpendicular to the line x + 2y = -8 is y = 2x - 15.

User Maximo
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