Question

Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Select two options.

Answer 1

Answer:

OPTION 2.

OPTION 5.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the line $3x - 4y = 7$, solve for "y":

$3x - 4y = 7\\\\-4y=-3x+7\\\\y=\frac{3}{4}x-\frac{7}{4}$

The slope of this line is:

$m=\frac{3}{4}$

Since the slopes of parallel lines are equal, the slope of the other line is:

$m=\frac{3}{4}$

Substitute the slope and the given point into $y=mx+b$ and solve for "b":

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

Then, the equation of this line in Slope-Intercept form is:

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

The equation of the line in Standard form is:

$Ax+By=C$

Then, manipulating the equation $y=\frac{3}{4}x+1$ algebraically, we get:

$y-1=\frac{3}{4}x\\\\4(y-1)=3x\\\\4y-4=3x\\\\-4=3x-4y\\\\3x-4y=-4$

Answer 2

Answer:

2 and 5

Step-by-step explanation:

The slope-intercept form of a line is y=mx-b where m is slope and b is y-intercept.

The point-slope form of a line is y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.

The standard form a line is ax+by=c.

So anyways parallel lines have the same slope.

So if we are looking for a line parallel to 3x-4y=7 then we need to know the slope of this line so we can find the slope of our parallel line.

3x-4y=7

Goal: Put into slope-intercept form

3x-4y=7

Subtract 3x on both sides:

  -4y=-3x+7

Divide both sides by -4:

   $y=\frac{-3}{-4}x+\frac{7}{-4}$

Simplify:

   $y=\frac{3}{4}x+\frac{-7}{4}$

So the slope of this line is 3/4.  So our line that is parallel to this one will have this same slope.

So we know our line should be in the form of $y=\frac{3}{4}x+b$.

To find b we will use the point that is suppose to be on our new line here which is (x,y)=(-4,-2).

So plugging this in to solve for b now:

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

$-2=-3+b$

$3-2=b$

$b=1$

so the equation of our line in slope-intercept form is $y=\frac{3}{4}x+1$

So that isn't option 1 because the slope is different.  That was the only option that was in slope-intercept form.

The standard form of a line is ax+by=c and we have 2 options that look like that.

So let's rearrange the line that we just found into that form.

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

Clear the fractions because we only want integer coefficients by multiplying both sides by 4.

This gives us:

$4y=3x+4$

Subtract 3x on both sides:

$-3x+4y=4$

I don't see this option either.

Multiply both sides by -1:

$3x-4y=-4$

I do see this as a option. So far the only option that works is 2.

Let's look at point slope form now.

We had the point that our line went through was (x1,y1)=(-4,-2) and the slope,m, was 3/4 (we found this earlier).

y-y1=m(x-x1)

Plug in like so:

y-(-2)=3/4(x-(-4))

y+2=3/4 (x+4)

So option 5 looks good too.