From 11:00PM PDT on Friday, July 1 until 5:00AM PDT on Saturday, July 2, the Shmoop engineering elves will be making tweaks and improvements to the site. That means Shmoop will be unavailable for use during that time. Thanks for your patience!
The slope of the line is -½, which will mean that it slopes downhill and is not very steep since the absolute value of the slope (|-½| is ½) is pretty small. We also know that it crosses the y-axis at -2. We will start by plotting the y-intercept and then counting over to the next point using a slope of -½.
Remember that slope equals rise/run, so this line changes 1 in the vertical direction for every 2 in the horizontal. Also, since it is a negative slope, make sure that you plot your points in the correct direction, downhill.
Graph the equation 4x + y = 7.
Unfortunately, this equation is not given to us in slope-intercept form ☹. However, we can solve the equation for y and manipulate it into this form.
subtract 4x from each side
switch the 7 and 4x, but keep the appropriate signs
Now you can see that the slope of this equation is , know as when written as a fraction, and the y-intercept is .
Graph the equation 2y = x.
Again, we will need to solve for y, since it is not in y = mx + b form.
divide each side by 2
remember that the coefficient in front of x is 1
Now we can see that the slope of the equations is ½, but where is b, the y-intercept? Can't find it? That's because it is 0; it's not necessary to write y = ½x + 0.
Let's plot a y-intercept of 0 and use the slope of ½ to find a few other points.
Find the equation of the line in slope-intercept form.
Let's look carefully at the graph and see if we can find any important information….
Ok, have you looked at it? You have, great! Then you noticed that the y-intercept is 1. We can also find the slope by counting the change in the vertical and horizontal directions between the two points shown (1 in the vertical and 3 in the horizontal). That gives a slope of 1/3.
Now, using that information we know these things:
b = 1 and m = 1/3
All we need to do is plug them into our equation, y = mx + b.