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Vinil7 [7]
3 years ago
9

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 s

ketch 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).

Mathematics
1 answer:
hammer [34]3 years ago
8 0

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:

<em><u>Question 1:</u></em>

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}

<em><u>Question 2:</u></em>

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

<em>      Finding the slope:</em>

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.

<em>      Finding the y-intercept:</em>

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

<em>      Writing the equation:</em>

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

<em><u>Question 3:</u></em>

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

<em>      Finding the y-intercept:</em>

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

<em>      Writing the equation:</em>

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

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