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?

Question

asked Jan 1, 2022 143k views

1 Answer

Dgangsta · Answer 1 · 2022-01-05T03:16:36+0000

Answer:

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

Explanation:

Hi there!

What we need to know:

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!