Standard form: graph an equation
key notes:
The x-intercept is the x-coordinate of the point where the graph crosses the x-axis. The coordinates of the x-intercept are (x,0), where x is the x-intercept.
The y-intercept is the y-coordinate of the point where the graph crosses the y-axis. The coordinates of the y-intercept are (0,y), where y is the y-intercept.
Learn with an example
Graph this line using intercepts:
2x+3y = 6
Step 1: Find the x-intercept.
The x-intercept is on the x-axis, where y=0. Plug y=0 into the equation and solve for the x-intercept x.
2x+3y=6
2x+3(0)=6 Plugin y=0
2x=6
x=3
The x-intercept is 3. Its coordinates are (3,0).
Step 2: Find the y-intercept.
The y-intercept is on the y-axis, where x=0. Plug x=0 into the equation and solve for the y-intercept y.
2x+3y=6
2(0)+3y=6 Plug in x=0
3y=6
y=2
The y-intercept is 2. Its coordinates are (0,2).
Step 3: Use the intercepts to graph.
Plot the x-intercept (3,0) and the y-intercept (0,2). The graph is the straight line connecting them.
Graph this line using intercepts:
8x–7y=56
Click to select points on the graph.
Step 1: Find the x-intercept.
The x-intercept is on the x-axis, where y=0. Plug y=0 into the equation and solve for the x-intercept x.
8x–7y= 56
8x–7(0) = 56 Plug in y=0
8x = 56 Simplify
x= 7 Divide both sides by 8
The x-intercept is 7. Its coordinates are (7,0).
Step 2: Find the y-intercept.
The y-intercept is on the y-axis, where x=0. Plug x=0 into the equation and solve for the y-intercept y.
8x–7y = 56
8(0)–7y = 56 Plugin x=0
–7y = 56 Simplify
y–8 Divide both sides by –7
The y-intercept is–8 Its coordinates are (0,–8).
Step 3: Use the intercepts to graph.
Plot the x-intercept (7,0) and the y-intercept (0, –8). The graph is the straight line connecting them.
Graph this line using intercepts:
2x+5y=–10
Click to select points on the graph.
Step 1: Find the x-intercept.
The x-intercept is on the x-axis, where y=0. Plug y=0 into the equation and solve for the x-intercept x.
2x+5y=–10
2x+5(0)=–10 Plugin y=0
2x–10 Simplify
x–5 Divide both sides by 2
The x-intercept is –5. Its coordinates are (–5,0).
Step 2: Find the y-intercept.
The y-intercept is on the y-axis, where x=0. Plug x=0 into the equation and solve for the y-intercept y.
2x+5y=–10
2(0)+5y=–10 Plugin x=0
5y–10 Simplify
y–2 Divide both sides by 5
The y-intercept is–2 Its coordinates are (0,–2).
Step 3: Use the intercepts to graph.
Plot the x-intercept (–5,0) and the y-intercept (0,–2). The graph is the straight line connecting them.
Let’s Practice!
