Answers:
1) The Equation of a Line is:
(1)
Where:
is the slope
is the y-intercept
For this problem we have a given
and a given ![b=4](https://tex.z-dn.net/?f=b%3D4)
So, we only have to substitute this values in the equation (1):
This is option B
2) Here we have to find the slope
and the y-intercept
of this equation:
According to the explanation in the first answer related to the equation (1), the slope of this line is:
![m=\frac{1}{5}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B5%7D)
And its y-intercept is:
![b=-8](https://tex.z-dn.net/?f=b%3D-8)
This is option C
3) We have to Equations of the Line, and we are asked if these are parallel:
(a)
(b)
Equation (b) has to be written in the same form of (a), in the form
in order to be able to compare both:
(c)
There is a rule that establishes that <em><u>Two lines are parallel if they have the same slope</u></em>. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then <u>they are not parallel</u>.
4) Here we are asked to write
in a standard form with integers:
![-\frac{3}{5}x+y=4](https://tex.z-dn.net/?f=-%5Cfrac%7B3%7D%7B5%7Dx%2By%3D4)
Multiply each side by 5:
![5(-\frac{3}{5}x+y)=5(4)](https://tex.z-dn.net/?f=5%28-%5Cfrac%7B3%7D%7B5%7Dx%2By%29%3D5%284%29)
![5(-\frac{3}{5}x)+5y=20](https://tex.z-dn.net/?f=5%28-%5Cfrac%7B3%7D%7B5%7Dx%29%2B5y%3D20)
![-3x+5y=20](https://tex.z-dn.net/?f=-3x%2B5y%3D20)
In this case none of the options apply, please check if the question was written correctly.
5) In this question we are asked to write an equation parallel to:
(2)
That passes through the given point (3,11). <u>(Notice that in the Cartesian plane the points have an x-component and a y-component)</u>
First, remember that <u>two Equations of the line are parallel when they have the same slope</u>. Now that this is clear, we are going to use the equation of the slope with the given point to find the parallel equation:
Equation of the slope:
(3)
From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):
Finally:
This is option B