Answer:
[tex]y=\frac{1}{2}x-7[/tex], or x-2y=14
Step-by-step explanation:
Hi there!
We want to find the equation of the line that passes through the point (2, -6) and is parallel to the line x-2y=8
First, we need to find the slope of x-2y=8, since parallel lines have the same slopes
We can convert the equation from standard form (ax+by=c) to slope-intercept form (y=mx+b, where m is the slope and b is the y intercept), in order to help us find the slope of the line
Start by subtracting x from both sides
-2y=-x+8
Divide both sides by -2
y=[tex]\frac{1}{2}x[/tex]-4
The slope of the line x-2y=8 is 1/2
It's also the slope of the line parallel to it.
Since we know the slope of the line, we can plug it into the equation for slope intercept form:
[tex]y=\frac{1}{2}x+b[/tex]
Now we need to find b.
As the equation of the line passes through (2, -6), we can use it to help solve for b
Substitute -6 as y and 2 as x:
[tex]-6=\frac{1}{2}(2)+b[/tex]
Multiply
-6=1+b
Subtract 1 from both sides
-7=b
Substitute -7 as b into the equation:
[tex]y=\frac{1}{2}x-7[/tex]
The equation can be left as that, or you can convert it into standard form if you wish.
In that case, you will need to move 1/2x to the other side:
[tex]-\frac{1}{2}x+y=-7[/tex]
A rule about the coefficients a, b, and c in standard form is that a (coefficient in front of x) CANNOT be negative, and every coefficient must be an integer (a whole number, not a fraction or decimal).
So multiply both sides by -2 in order to clear the fraction, as well as change the sign of a
x-2y=14
Hope this helps!
