which equation has a graph perpendicular to the graph of 7x
=14y-8?
To find an equation that has a graph perpendicular to the graph of 7x = 14y - 8, we need to find the slope of the line given by 7x = 14y - 8.
Let's begin by converting the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Starting with the equation 7x = 14y - 8, we isolate y to one side:
7x = 14y - 8
7x + 8 = 14y
(7/14)x + (8/14) = y
(1/2)x + (4/7) = y
Now we can identify the slope of the original line: m = 1/2.
To find the slope of a line perpendicular to the original line, we need to take the negative reciprocal of the original slope.
The negative reciprocal of 1/2 is -2/1 = -2.
Therefore, the equation with a graph perpendicular to the graph of 7x = 14y - 8 will have a slope of -2.
To find an equation that has a graph perpendicular to the graph of 7x = 14y - 8, we first need to determine the slope of the given line.
We can rewrite the equation in slope-intercept form (y = mx + b) by solving for y:
7x = 14y - 8
14y = 7x + 8
y = (7/14)x + 8/14
y = (1/2)x + 4/7
Comparing the equation to the slope-intercept form, we can see that the slope (m) of the given line is 1/2.
Perpendicular lines have slopes that are negative reciprocals of each other. So, the slope of the line perpendicular to the given line would be -2 (the negative reciprocal of 1/2).
Now that we have the slope, we can write the equation of the line perpendicular to the given line using the point-slope form (y - y1 = m(x - x1)), where (x1, y1) is any point on the line.
Let's say we want to find the equation of the line passing through the point (0, 0):
Using the point-slope form:
y - 0 = -2(x - 0)
y = -2x
Therefore, the equation of the line perpendicular to the graph of 7x = 14y - 8 is y = -2x.
To find the equation that has a graph perpendicular to the given graph of 7x = 14y - 8, we need to find the equation of a line that is perpendicular to it.
First, let's convert the given equation into slope-intercept form (y = mx + b) by solving for y:
7x = 14y - 8
14y = 7x + 8
y = (7/14)x + (8/14)
y = (1/2)x + (4/7)
In slope-intercept form, we can see that the slope of the given line is 1/2.
To find the slope of a line perpendicular to this one, we need to take the negative reciprocal of the slope. The negative reciprocal of 1/2 is -2.
Now, we have the slope (-2), and to find the equation of a line with this slope, we also need a point. Let's choose the point (0,0) as an example.
Using the point-slope form (y - y1 = m(x - x1)), we can plug in the values:
y - 0 = -2(x - 0)
y = -2x
Therefore, the equation that has a graph perpendicular to the graph of 7x = 14y - 8 is y = -2x.