Respuesta :
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:
[tex]y=\frac{-3}{-4}x+\frac{7}{-4}[/tex]
Simplify:
[tex]y=\frac{3}{4}x+\frac{-7}{4}[/tex]
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 [tex]y=\frac{3}{4}x+b[/tex].
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:
[tex]-2=\frac{3}{4}(-4)+b[/tex]
[tex]-2=-3+b[/tex]
[tex]3-2=b[/tex]
[tex]b=1[/tex]
so the equation of our line in slope-intercept form is [tex]y=\frac{3}{4}x+1[/tex]
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.
[tex]y=\frac{3}{4}x+1[/tex]
Clear the fractions because we only want integer coefficients by multiplying both sides by 4.
This gives us:
[tex]4y=3x+4[/tex]
Subtract 3x on both sides:
[tex]-3x+4y=4[/tex]
I don't see this option either.
Multiply both sides by -1:
[tex]3x-4y=-4[/tex]
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.
Answer:
OPTION 2.
OPTION 5.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Given the line [tex]3x - 4y = 7[/tex], solve for "y":
[tex]3x - 4y = 7\\\\-4y=-3x+7\\\\y=\frac{3}{4}x-\frac{7}{4}[/tex]
The slope of this line is:
[tex]m=\frac{3}{4}[/tex]
Since the slopes of parallel lines are equal, the slope of the other line is:
[tex]m=\frac{3}{4}[/tex]
Substitute the slope and the given point into [tex]y=mx+b[/tex] and solve for "b":
[tex]-2=\frac{3}{4}(-4)+b\\\\-2+3=b\\\\b=1[/tex]
Then, the equation of this line in Slope-Intercept form is:
[tex]y=\frac{3}{4}x+1[/tex]
The equation of the line in Standard form is:
[tex]Ax+By=C[/tex]
Then, manipulating the equation [tex]y=\frac{3}{4}x+1[/tex] algebraically, we get:
[tex]y-1=\frac{3}{4}x\\\\4(y-1)=3x\\\\4y-4=3x\\\\-4=3x-4y\\\\3x-4y=-4[/tex]
