Find an equation of the line. Write the equation in the standard form.
Through (7,6); parallel to 4x-y=9
Parallel lines have the same slope.
Find the slope of 4x-y=9
Use the new slope to obtain
y = mx + b, that is
y = 4x + b then sub in your (x,y) that is (7,6) and solve for b : ) as you are passing through that point.
Then your equation is y=4x +b (with whatever b you found)
Now just put that into standard form.
To find the equation of the line that is parallel to the given line and passes through the given point, we need to follow a few steps.
First, let's rewrite the given equation, 4x - y = 9, in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Rearranging the equation, we have:
y = 4x - 9
Since the line we want to find is parallel to this line, it will have the same slope. Therefore, the slope of the new line will be 4.
Now, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) represents the given point and m is the slope.
Plugging in the values we have, the point-slope form becomes:
y - 6 = 4(x - 7)
Expanding and simplifying the equation, we get:
y - 6 = 4x - 28
To write the equation in standard form, we need to rearrange it so that all variables are on the left side and the constant term is on the right side. So, let's bring the x-term to the left and simplify:
4x - y = 6 - 28
4x - y = -22
Therefore, the equation of the line, in standard form, that passes through the point (7, 6) and is parallel to the line 4x - y = 9 is 4x - y = -22.