How to find the gridient of a graph?

Question

I have some graphing questions that I am not sure of.

First, I was supposed to plot the graph of y = 3x+3, which I think I did that right after some help, but now I have to figure out the gradient, y intercept, and x intercept of the graph.

I think the y intercept is 3 and the x intercept is -1. Are those right? I still don't know how to find the gradient though.

And the last part of the question is to consider the equation y = -1/3x+3 (-1/3 is a fraction not the division symbol). Explain the differences/similarities between this graph and the previous graph?

Can anyone help?

Thanks.

Answer 1

If y = ax + b, b is the y intercept and a is the slope, which you call the gradient. So in y = 3x + 3, the gradient is the 3 in front of x. You get the y intercept by letting x = 0 and solving for y:

y = 3(0) + 3 = 3

and you get the x intercept by letting y = 0 and solving for x:

0 = 3x + 3
-3 = 3x
-1 = x.

y = (-1/3)x + 3 has the same y intercept as the first equation, but here the slope is negative, downhill. More -- the 2 lines are perpendicular, which happens whenever the 2 gradients multiplied together = -1. And of course, the x intercept:

0 = (-1/3)x + 3
-3 = (-1/3)x
9 = x

Answer 2

Yes, you find the intercepts by setting x to 0 and solving for y and vice versa. So y = 3 and x = -1 for those cases.

I'm not sure about the terminology but perhaps gradient is just the slope of the line.

For the last question you should probably draw the two graphs and talk about the two lines in terms of the coefficient of x and the sign.

Answer 3

I believe you have perpendicular lines intersecting at y-axis. All your answers are right for 1st equation.(The fraction in front of x variable represents slope rise/run)