Finding intercepts helps with graphing any function. It is extra helpful with linear functions of two variables, because once the intercepts have been found, the graph can be sketched directly from these results.
You just need to find any two points on a line to be able to sketch it, and the intercepts are often easiest.
Once you have found a couple of points connect with a straight line passing through both.
Step 0: (Assuming the equation is linear) Check whether both x and y are in the equation. If either is missing:
the line is either parallel to or on the axis whose variable was missing. Congratulations! You are done.
For your 2 points, pick any 2 values you want for the missing variable, plot the points using the equation
to determine the value of the variable that wasn't missing.
Step 1: To find where (if anywhere) the graph passes through the y-axis, set x = 0 and solve the equation to get y by itself.
---> "set x = 0" means replace all the instances of where x occurs in the formula by a zero.
SKIP THIS ALGEBRA OVER-EXPLANATION IF YOU ALREADY UNDERSTAND SOLVING FOR A SINGLE VARIABLE
So (since the question was using the notational convention that multiplication is implied when you see two factors written right next to one another), after setting x to zero, our equation reads:
5*(0) = 3*y + 15
But 5*0 is? 0 (of course!)
so it also is saying
0 = 3*y + 15
To solve for y means we isolate it to condense the facts into simpler versions of themselves. There are two operations happening in this equation and we need to undo both of them to get the simplest version of the statement about y that still means the same thing as the current statement.
By doing the same thing to both sides of an equation or inequality, we make sure we are not changing the facts it states -- just re-stating the same facts in a different way.
We can subtract 15 from both sides to undo the addition, and we can divide both sides by 3 to undo the multiplication by 3.
Let's suppose we decide to do the subtraction first (although it doesn't really matter --- if done correctly, the same results come out regardless)
On the left side 0-15 = -15 and on the right side, 3y+15 -15 = 3y
Then as we subtracted first all we still have left to do is divide both sides by 3. Right?
-15 / 3 = -5 and 3*y/3 = y.
-5 = y
or
END OF "SKIP THIS ALGEBRA OVER-EXPLANATION IF YOU ALREADY UNDERSTAND SOLVING FOR A SINGLE VARIABLE"
y = -5
Thus for this linear equation, when x is zero, y has to be -5. In other words, the y-intercept is -5. So (x,y) = (0,-5) is one of the two points we need to sketch this line. We just need one more point (see Step 2 below).
Step 2: Set y = 0 and solve for x to find the x-intercept.
5x = 3*0 + 15
5x = 15
x=? You do the rest!
This answer goes into the x-coordinate of the second point (x,y) = (your answer, 0) since we set y=0... we did this because we are looking for the x-intercept (on the x-axis, where y is always zero no matter where you check on that axis -- all the points on it are zero units of distance from it in the y-direction)
