Question

Using complete sentences, explain how to graph y = negative one fifthx - 2 using the slope-intercept method.

Answer 1

Any ideas?

Answer 2

$$y=\frac{1}{5}x-2$$

Answer 3

Remember, in slope-intercept form, y = mx + b, m is the slope, and b is the y-intercept, the point at which the line crosses the y-axis. Slope is the ratio of change in y to change in x. A slope of -1/5 means that for y to change by -1, x has to change by 5. This is a line that is nearly horizontal, sloping down gradually to the right.

Answer 4

Thank you, but how do I know where to graph it?

Answer 5

@whpalmer4

Answer 6

Well, you know 1 point: (0, y-intercept) = (0, -2). So the line goes through that point, and it slopes down and to the right, dropping 1 unit on the y-axis for every 5 units moved to the right on the x-axis. Another point would be (0+5, -2-1) = (5, -3). Draw your line through those points. Or, rearrange your equation into standard form, which has x and y on the left side, and a number on the right side:
\[Ax + By = C\]which in this case is\[y - \frac{1}{5}x = -2\] (I subtracted x/5 from both sides) or more conveniently after multiplying both sides by 5\[5y - 1x = -10\]The nice thing about standard form is it makes drawing the line easy. The x-intercept (y = 0) is (C/A, 0) and the y-intercept is (0, C/B), so you just plot those points and draw a straight line through them.

Answer 7

For your formula, A = -1, B = 5, C = -10:

\[-1x + 5y = -10\]
(I should have written in that order, sorry)

Answer 8

I thought it was something like, m = y1 - y2 over x1 - x2

Answer 9

Yes, that is a formula for determining the slope between two points.

Answer 10

\[m =\frac{ y1 - y2 }{ x1 - x2 }\]

Answer 11

But we already know the slope, because our equation was in slope-intercept form: y = mx + b

Answer 12

Ok then for my answer to: Using complete sentences, explain how to graph y = -1/5x - 2 using the slope-intercept method.
What should I type in the box?

Answer 13

Well, as I said, you identify the slope from the equation, and the y-intercept to fix a point on the line. Then you draw a line through that point with the slope you found.

Answer 14

Remember, the y-intercept is the point at which the line crosses the y-axis, meaning x = 0, so you'll know that (0, b) is a point on the line. y = mx + b, y = m(0) + b, y = b at the y-intercept.

Answer 15

Im so confused :S Sorry I just dont get it

Answer 16

Will you just tell me what you would put in the answer box if you were taking the quiz.

Answer 17

Trust me, you do need to understand this unless this is the very last math quiz you'll ever take :-)

Which part don't you understand?

Answer 18

I understand everything except how to put it on the graph.

Answer 19

What do you need to know to put it on the graph?

Answer 20

x adn y intercepts, which is -1/5 and -2

Answer 21

Well, that's one way to do it. You know the y-intercept already. You could find the x-intercept using the equation for the line and the knowledge that the x-intercept is where y = 0.

But my interpretation of the question is that they want you to use the y-intercept and the slope to graph it. You know the y-intercept. You know the slope. You just need to know what the slope means when you draw the line. I'm guessing you don't have a feel for what the slope means in terms of a graph. Here are some examples:

slope of 1 (m = 1) gives a graph that goes up at a 45 degree angle. Every 1 step to the right, you go up 1 step.

slope of =1 (m = -1) gives a similar graph, but it goes down at a 45 degree angle. Every 1 step to the right, you go down 1 step.

If you draw two lines, one with slope 1, and another with slope -1, you get a nice symmetrical X on your graph. The definition of perpendicular lines is that the product of their slopes = -1.

A slope which is > 1 means that the line goes up faster than it goes to the right. A slope of 2, for example, goes up by 2 steps for every step to the right.

A slope which is < 1 (but > 0) means that the line goes up slower than it goes to the right. A slope of 1/2 goes up 1 step for every 2 steps to the right.

A negative slope behaves like the positive slope would, except that it goes in the opposite direction. A slope of -2 goes down faster than it does to the right, going down 2 steps for every step to the right. A slope of -1/2 goes down 1 step for every 2 steps to the right.

Answer 22

So, plot the point for the y-intercept, then move over and up/down the appropriate number of steps for the slope, plot that point, and draw a straight line through them.

Answer 23

Ok thanks for you help but I think Im more confused now than I was before. Guess Ill just try and figure it out myself :S