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.