Check your answers below.
For each of these graphs, look for the slope and the y-intercept.
In the function y = 2x,
The slope is 2, since 2 is being multiplied to x.
The y-intercept is 0. There is no number being added or subtracted, so we automatically assume that b (the y-intercept) is 0.
In the function y = x + 1,
The slope is 1. We don't see any number being multiplied to x, but I'm sure you know that we can just write a 1 in front of x and say it's being multiplied by 1.
The y-intercept is 1, since 1 is being added to x.
In the function y = 2x + 1,
The slope is 2.
The y-intercept is 1.
And in the function y = 2/3x + 1,
The slope is 2/3.
The y-intercept is 1.
Now, we graph these lines.
To graph the function y = 2x:
Make a point at the y-intercept, which we know is 0. From this dot, use the slope to find the next point. The slope is 2, which is a whole number. We can write it as a fraction by dividing it by 1, so it can be written as 2/1. Since slope is 'rise' over 'run', you need to 'rise' up 2 units and 'run' over (to the right) 1 unit. If you've done this correctly you should have made a dot at the point (1,2). All you need to draw your line is two points and now we have 2 points, (0,0) and (1,2). Just draw your line between these points.
To graph the function y = x + 1:
The y-intercept is 1, so make a dot on the y-axis at y = 1. Now use the slope, which is 1, to find the next point. The slope can be written as 1/1 (just divide 1 by 1), so 'rise' up 1 unit and 'run' over 1 unit. You should now have a dot on the point (1,2). Now just draw your line between the two points you have (0,1) and (1,2).
To graph the function y = 2x + 1:
Make a dot at y = 1. Use the slope, 2, which we can write as 2/1, to find the next point. 'Rise' up 2 units and 'run' over 1 unit. You should now have a point at (1,3) and (0,1). Now draw your line.
To graph the function y = 2/3x + 1:
Start at the y-intercept, which is 1. Now use the slope 2/3 and 'rise' 2 units, 'run' 3 units. Your points should now be at (0,1) and (3,3). Draw your line.
ThePerfectHacker was kind enough to show the graphs