Question

PLEASE HELP 15 POINTS 1. An architect is drawing a sketch for a new building. He uses graphs of lines on a coordinate plane to sketch out
his ideas. The architect has plotted the graph of the line 4x + 16y = 8.
What is the equation of the line he has graphed in slope-intercept form? (Reduce all fractions)
2
Write the equation in slope-intercept form perpendicular to the original line that goes through the point
(-6, -19)
3
Write the equation in slope-intercept form parallel to the original line that goes through the point (-8,6).

Answer 1

Answer:

1) $y=-\frac{1}{4}x+\frac{1}{2}$

2) $y=4x+5$

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

Step-by-step explanation:

Question 1:

All you have to do is solve for y to get the slope intercept form.

$4x+16y=8\\16y=-4x+8\\y=-\frac{1}{4}x+\frac{1}{2}$

So the equation is $y=-\frac{1}{4}x+\frac{1}{2}$

Question 2:

Now for this one you have to find the line perpendicular to the previous equation.

     Finding the slope:

So first we need to find the slope and usually the slope of a perpendicular line is the opposite and the reciprocal to the original equation. So instead of $-\frac{1}{4}$ it will be $\frac{4}{1}$ or even easier to manage $4$.

     Finding the y-intercept:

For the y-intercept we need to plug in what we know into this formula....$y=mx+b$

We know the slope is $4$ and we could use the ordered pair that they provided us with $(-6,-19)$. The -6 is the x and the -19 will be the y. Now let's plug in and solve.

$y=mx+b\\-19=4(-6)+b\\-19=-24+b\\b=5$

     Writing the equation:

Now we know all the information needed to write the equation.

$y=mx+b\\m=4\\b=5$

Now we just fill it in the formula...

$y=4x+5$

Question 3:

For a parallel equation the slope will be the same in order for them to be parallel to each other.

     Finding the y-intercept:

For the y-intercept we need to plug in what we know into this formula....$y=mx+b$

We know the slope is $-\frac{1}{4}$ and we could use the ordered pair that they provided us with $(-8,6)$. The -8 is the x and the 6 will be the y. Now let's plug in and solve.

$y=mx+b\\6=-\frac{1}{4}(-8)+b\\6=2+b\\b=4$

     Writing the equation:

Now we know all the information needed to write the equation.

$m=-\frac{1}{4}\\b=4$

Now we just fill it in the formula...

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