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44 votes
Write an equation for a line parallel to 4x – 2y = 4 that passes through the point (3,22)

User Kieren Johnstone
by
2.4k points

2 Answers

23 votes
23 votes

Answer:

y = 2x + 16

Explanation:

4x - 2y = 4

-2y = -4x + 4

y = -4/-2x + 4/-2

y = 2x - 2

Slope: 2

Point: (3,22)

y-intercept: 22 - (2)(3) = 22 - 6 = 16

User LHMathies
by
3.1k points
16 votes
16 votes

Answer:

y=2x+16 or 2x-y=-16

Explanation:

Hi there!

We are given the equation 4x-2y=4, and we want to write an equation for the line parallel to it, that also passes through (3, 22)

First, let's find the slope of the line, as parallel lines have the same slope.

In order to find the slope, we can convert the equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

Start by subtracting 4x from both sides:

-2y=-4x+4

Divide both sides by -2

y=2x-2

2 is in the place where x is, so the slope of the line is 2

It's also the slope of the line parallel to it.

Writing the equation in slope-intercept form, this is the equation so far:

y=2x+b

Now let's find b

Since the equation passes through the point (3,22), we can use it to help solve for b

Substitute 22 as y and 3 as x:

22=2(3)+b

Multiply

22=6+b

Subtract 6 from both sides

16=b

Substitute 16 as b in the equation.

y=2x+16

We can stop right here, but we can also re-convert it into standard form

To do that, subtract 2x from both sides:

-2x+y=16

There's a rule that the coefficient in front of x CANNOT be negative; in order to change the sign, multiply both sides of the equation by -1

2x-y=-16

Hope this helps!

User Kean Amaral
by
3.2k points