Write an equation of the line that is parallel to the graph of y=7x -3 and passes through the origin
slope is 7, so
y-0 = 7(x-0)
or,
y=7x
Well, if we want a line that is parallel to the graph of y = 7x - 3, we know that the slope of the new line must be the same, since parallel lines have the same slope. So the slope of our new line is 7.
To find the equation of a line, we need the slope and a point on the line. We're given that the new line passes through the origin, which is the point (0, 0).
Using the point-slope form of an equation, we have:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope. Plugging in the values we have, we get:
y - 0 = 7(x - 0).
Simplifying this equation, we get:
y = 7x.
So, the equation of the line that is parallel to the graph of y = 7x - 3 and passes through the origin is y = 7x.
To find an equation of a line parallel to the graph of y = 7x - 3 and passes through the origin, we need to determine the slope of the given line.
In the equation y = 7x - 3, the coefficient of x is the slope, which is 7.
Since a line parallel to the given line will have the same slope, the equation of the line passing through the origin can be written as y = mx, where m is the slope.
In this case, the slope (m) is 7, so the equation of the line that is parallel to the graph of y = 7x - 3 and passes through the origin is:
y = 7x
To find the equation of a line parallel to a given line and passing through a specific point, you need to use the slope-intercept form of the equation of a line:
y = mx + b
where:
m is the slope of the line, and
b is the y-intercept of the line.
To determine the slope (m) of the line, you must know that parallel lines have the same slope. In the given equation, y = 7x - 3, the slope is 7.
Since the line passes through the origin (0,0), you have a point (x₁,y₁) = (0,0) on the line. So, you have x₁ = 0 and y₁ = 0.
Using these values, you can substitute them into the slope-intercept form and solve for the y-intercept (b):
0 = 7(0) + b
0 = 0 + b
b = 0
Now, you have determined the slope (m = 7) and the y-intercept (b = 0). Plugging these values into the slope-intercept form, you can write the equation of the line:
y = 7x + 0
y = 7x
Therefore, the equation of the line parallel to y = 7x - 3 and passing through the origin is y = 7x.