Question

1). Write an equation of a line with the given slope and y-intercept.

Answer 1

Answers:

1) The Equation of a Line is:

$y=mx+b$    (1)

Where:

$m$ is the slope

$b$ is the y-intercept

For this problem we have a given $m=-2$ and a given $b=4$

So, we only have to substitute this values in the equation (1):

$y=-2x+4$    

This is option B

2) Here we have to find the slope $m$ and the y-intercept $b$ of this equation:

$y=\frac{1}{5}x-8$    

According to the explanation in the first answer related to the equation (1), the slope of this line is:

$m=\frac{1}{5}$

And its y-intercept is:

$b=-8$

This is option C

3) We have to Equations of the Line, and we are asked if these are parallel:

$y=6x+9$    (a)

$27x-3y=-81$    (b)

Equation (b) has to be written in the same form of (a), in the form $y=mx+b$ in order to be able to compare both:

$-3y=-81-27x$    

$y=-\frac{1}{3}(-81-27x)$    

$y=\frac{81}{3}+\frac{27}{3}x$    

$y=9x+27$    (c)

There is a rule that establishes that Two lines are parallel if they have the same slope. In this case, if we compare equations (a) and (c) we find they don’t have the same slope, then they are not parallel.

4) Here we are asked to write $y=\frac{3}{5}x+4$ in a standard form with integers:

$-\frac{3}{5}x+y=4$

Multiply each side by 5:

$5(-\frac{3}{5}x+y)=5(4)$

$5(-\frac{3}{5}x)+5y=20$

$-3x+5y=20$

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:

$y=2x+7$     (2)

That passes through the given point (3,11). (Notice that in the Cartesian plane the points have an x-component and a y-component)

First, remember that two Equations of the line are parallel when they have the same slope. 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:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$    (3)

From (2) we know the slope is 2, then we only have to substitute this value and the points in (3):

$2=\frac{y-11}{x-3}$    

$2(x-3)=y-11$      

$2x-6=y-11$      

Finally:

$y=2x+5$      

This is option B