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

1)
`y=-(1)/(4)x+(1)/(2)`

2)
`y=4x+5`

3)
`y=-(1)/(4)x+4`

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=-(1)/(4)x+(1)/(2)`

So the equation is
`y=-(1)/(4)x+(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
`-(1)/(4)` it will be
`(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
`-(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=-(1)/(4)(-8)+b\\6=2+b\\b=4`

Writing the equation:

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

`m=-(1)/(4)\\b=4`

Now we just fill it in the formula...

`y=-(1)/(4)x+4`