The equation of line L is y=3x–4 and is perpendicular to line H. They cross each other at the y-intercept of line L. Find the equation of line H.
The y-intercept of L is y=3x–4 is (0,-4)
the slope of L is 3
so the slope of H is -1/3
equation of H:
y + 4 = (-1/3)x
y = (-1/3)x - 4
To find the equation of line H, which is perpendicular to line L and crosses at the y-intercept of line L, we need to determine the slope of line H.
The given equation of line L is y = 3x - 4. We can see that the slope of line L is 3.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of line H will be the negative reciprocal of 3, which is -1/3.
We know that line H crosses at the y-intercept of line L, which is -4. This is because the y-intercept is the point where the line intersects the y-axis, and in the equation y = 3x - 4, the y-intercept is -4.
Now we can use the slope-intercept form of a line to find the equation of line H, which is given by y = mx + b, where m is the slope and b is the y-intercept.
Therefore, the equation of line H is y = -1/3 x - 4.
To find the equation of line H, we need to determine its slope.
Since line L is given by the equation y = 3x - 4, we can identify its slope as the coefficient of x, which is 3.
According to the question, line H is perpendicular to line L. In this case, the slopes of the two lines are negative reciprocals of each other.
To find the negative reciprocal of 3, we can flip the fraction and change its sign. So the slope of line H will be -1/3.
Now, we have the slope of line H, but we still need to find the y-intercept.
The question states that line L and line H cross each other at the y-intercept of line L. Since the y-intercept is the point where the line intersects the y-axis, it has an x-coordinate of 0.
Substituting x = 0 into the equation of line L, we get y = 3(0) - 4 = -4. Therefore, the y-intercept of line L is (0, -4).
Now we have the slope (-1/3) and the y-intercept (0, -4) of line H. We can write the equation of line H using the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Substituting the slope and the y-intercept values, the equation of line H is y = (-1/3)x - 4.