Answer:
y=2x+16 or 2x-y=-16
Step-by-step explanation:
Hi there!
We are given the equation 4x-2y=4, and we want to write an equation for the line parallel to it, that also passes through (3, 22)
First, let's find the slope of the line, as parallel lines have the same slope.
In order to find the slope, we can convert the equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).
Start by subtracting 4x from both sides:
-2y=-4x+4
Divide both sides by -2
y=2x-2
2 is in the place where x is, so the slope of the line is 2
It's also the slope of the line parallel to it.
Writing the equation in slope-intercept form, this is the equation so far:
y=2x+b
Now let's find b
Since the equation passes through the point (3,22), we can use it to help solve for b
Substitute 22 as y and 3 as x:
22=2(3)+b
Multiply
22=6+b
Subtract 6 from both sides
16=b
Substitute 16 as b in the equation.
y=2x+16
We can stop right here, but we can also re-convert it into standard form
To do that, subtract 2x from both sides:
-2x+y=16
There's a rule that the coefficient in front of x CANNOT be negative; in order to change the sign, multiply both sides of the equation by -1
2x-y=-16
Hope this helps!
