Question

What is an equation of the line that passes through the point (2,−6) and is parallel to the line x-2y=8

Answer 1

Answer:

$y=\frac{1}{2}x-7$, 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=$\frac{1}{2}x$-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:

$y=\frac{1}{2}x+b$

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:

$-6=\frac{1}{2}(2)+b$

Multiply

-6=1+b

Subtract 1 from both sides

-7=b

Substitute -7 as b into the equation:

$y=\frac{1}{2}x-7$

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:

$-\frac{1}{2}x+y=-7$

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!