Question

5)Write the equation of a line,which is parallel to 2x -4y =12 and passing through the point (4,3) in standard form using integers?

Answer 1

`y=(1)/(2) x+1`

Explanation:

Hi there!

What we need to know:

• Parallel lines have the same slope and different y-intercepts

1) Determine the slope (m)

Rewrite
`2x -4y =12` in slope-intercept form. This will make it easier for us to identify the slope.

Slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

`2x -4y =12`

Subtract 2x from both sides to isolate -4y

`2x -4y-2x =-2x+ 12\\-4y=-2x+ 12`

Divide both sides by -4 to isolate y

`-4y=-2x+ 12\\y=(1)/(2)x -3`

Now, we can see clearly that
`(1)/(2)` is in the place of m in
`y=mx+b` , making it the slope of the line.

Because parallel lines have the same slopes, we know that the line we're determining will also have a slope of
`(1)/(2)`.

2) Determine the y-intercept (b)

Plug
`(1)/(2)` into
`y=mx+b`

`y=(1)/(2) x+b`

Plug in the given point (4,3)

`3=(1)/(2) (4)+b\\3=2+b`

Subtract 2 from both sides

`3-2=2+b-2\\1=b`

Therefore, the y-intercept (b) is 1. Plug this back into
`y=(1)/(2) x+b`

`y=(1)/(2) x+1`

I hope this helps!