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

Answer:

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

Step-by-step 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

$-4y=-2x+ 12\\y=\frac{1}{2}x -3$

Now, we can see clearly that $\frac{1}{2}$ 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 $\frac{1}{2}$.

2) Determine the y-intercept (b)

Plug $\frac{1}{2}$ into $y=mx+b$

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

Plug in the given point (4,3)

$3=\frac{1}{2} (4)+b\\3=2+b$

Subtract 2 from both sides

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

Therefore, the y-intercept (b) is 1. Plug this back into $y=\frac{1}{2} x+b$

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

I hope this helps!