Graphing a Linear Equation Using Intercepts
Graph a linear equation using x and y intercepts: set y=0 to find the x-intercept, set x=0 to find the y-intercept, plot both points, then draw the line through them.
Key Concepts
Find the $x$ intercept by setting $y = 0$ and solving for $x$. Then, find the $y$ intercept by setting $x = 0$ and solving for $y$. Plot these two points and draw a straight line through them.
To graph $4x 2y = 8$: For the $x$ intercept, set $y=0$ to get $4x=8$, so $x=2$. The point is $(2, 0)$. For the $y$ intercept, set $x=0$ to get $ 2y=8$, so $y= 4$. The point is $(0, 4)$. Plot and connect $(2, 0)$ and $(0, 4)$. To graph $ x + 3y = 6$: For the $x$ intercept, set $y=0$ to get $ x=6$, so $x= 6$. The point is $( 6, 0)$. For the $y$ intercept, set $x=0$ to get $3y=6$, so $y=2$. The point is $(0, 2)$. Plot and connect $( 6, 0)$ and $(0, 2)$.
Why hunt for a bunch of points when you only need two? The intercepts are the line's special 'touchdown' spots on the axes. Finding them is the fastest way to get your line on the graph and score a perfect plot!
Common Questions
What are the x-intercept and y-intercept of a linear equation?
The x-intercept is the point where the line crosses the x-axis, which occurs when y=0. The y-intercept is where the line crosses the y-axis, which occurs when x=0. Together these two intercepts provide two distinct points that define the line.
How do you graph a linear equation using intercepts?
Set y=0 and solve for x to find the x-intercept (x, 0). Set x=0 and solve for y to find the y-intercept (0, y). Plot both intercepts on the coordinate plane. Draw a straight line through both points and extend it with arrows in both directions.
What should you do if both intercepts are at the origin?
If setting y=0 gives x=0 and setting x=0 gives y=0, both intercepts are at the same point (the origin). The line passes through the origin, so you need a second point. Substitute any nonzero x-value, compute y, plot that point, and draw the line through the origin and that point.