A line has x-intercept (5, 0) and is perpendicular to the line 2x + 8y = 10. Find the y-intercept of the line.
your given line of 2x + 8y = 10 has slope -2/8 or -1/4
so the slope of a perpendicular line is +4
its equation is y = 4x + b, but (5,0) lies on it, so
0 = 4(5) + b
b = -20
new equation: y = 4x - 20
and the y-intercept is -20, (since we have it in slope y-intercept form)
Well, you know, when it comes to math and humor, I guess you could say I'm pretty acute. So let's take a funny look at this problem.
To find the y-intercept of a line, we need its equation in the form y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the given line, let's rewrite it in the slope-intercept form. We rearrange the equation and isolate y:
2x + 8y = 10
8y = -2x + 10
y = (-2/8)x + 10/8
y = (-1/4)x + 5/4
Now, since the given line is perpendicular to the line we want to find, the slopes are negative reciprocals of each other. So the slope of the line we're looking for is 4/1 or simply 4.
Now we can use the slope-intercept form, since we have the slope. The line's equation is y = 4x + b, where b is the y-intercept that we're trying to find.
Since the line passes through the point (5, 0), we can substitute these values into the equation to solve for b:
0 = 4(5) + b
0 = 20 + b
b = -20
So the y-intercept of the line is -20. And there you have it—a y-intercept tale full of math and humor!
To find the equation of the line perpendicular to the line 2x + 8y = 10, we need to determine the slope of the given line first.
Step 1: Convert the given equation to slope-intercept form (y = mx + b):
2x + 8y = 10
8y = -2x + 10
y = (-2/8)x + 5/4
y = (-1/4)x + 5/4
The slope of the given line is -1/4.
Step 2: Determine the slope of the line perpendicular to the given line. Perpendicular lines have slopes that are negative reciprocals of each other. That means the slope of the perpendicular line will be the negative reciprocal of -1/4, which is 4.
Step 3: Use the slope-intercept form of a line (y = mx + b), with the known x-intercept (5, 0) to find the y-intercept (b).
Using the point-slope form, we have:
y - y1 = m(x - x1)
y - 0 = 4(x - 5)
y = 4x - 20
Therefore, the y-intercept of the line is -20.
To find the equation of a line perpendicular to another line, we need to know the slope of the original line. The slope of a line can be found by rearranging the equation of the line into slope-intercept form (y = mx + b), where m is the slope.
Given the equation 2x + 8y = 10, we can rewrite it in slope-intercept form:
8y = -2x + 10
y = (-2/8)x + 10/8
y = (-1/4)x + 5/4
From the equation, we can see that the slope of the original line is -1/4.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the line we're looking for is the negative reciprocal of -1/4, which is 4/1 or simply 4.
Now that we have the slope (m = 4) and the x-intercept (5,0), we can use the point-slope form of a line (y - y1 = m(x - x1)) to find the equation of the line:
y - 0 = 4(x - 5)
y = 4x - 20
The y-intercept represents the point where the line intersects the y-axis. To find it, we set x = 0 in the equation:
y = 4(0) - 20
y = -20
Therefore, the y-intercept of the perpendicular line is -20.