Question

8x-y=16

Find the slope and y-intercept of the line with the given equation. Write a complete solution, showing all steps used in finding the slope and y-intercept and post it to the discussion board. What is the slope and what does it mean? What is the y-intercept and what does it mean?  Explain each step as if you were the expert explaining it to a novice.

Answer 1

Hello,

the general formula of the line is: y=mx+b

where "m" is the slope of the function. So we have to put our function in this form in order to find the slope, so:

8x-y=16
8x=16+y
8x-16=y
y=8x-16

Then: m=8

The positive slope implies that the function is increasing, if the slope is negative, the function is decreasing as I show you in the picture.

Now, if we want to get the y-intercept of the function we have to analyze that the function intersects the "y" axis when x=0, so we replace x=0 in the function and find y:

8*(0)-y=16
-y=16
y=-16

Answer: m=8 and y-intercept=-16

Answer 2

The Equation 8x-y=16 is in what is called standard form. It is Written as Ax+By=C. We need to get to slope intercept form to answer the question. Slope intercept is Y=mx+b. M stands for the slope and B is the Y-intercept. We need to isolate Y on one side of the equation:

8x-y=16 Subtract 8x to isolate Y
-y=16-8x

Now we need to make Y positive, so we multiply the whole equation by -1

-1(-y)=-1(16)-1(-8x)
Y=-16+8x
Rewrite this in slope intercept to get:
Y=8x-16

The slope (m) is 8. The slope if the rise over run over the line. Say the line goes from (0,0) to (2,2), the slope would be 1 because 2/2=1

-16 is the y-intercept. When x=0, y=-16

I hope this helps. I can clarify any confusing steps.