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Equations such as $y=x+2$ are called linear equations. In this lesson you will study this and other similar equations, learn about their graphs, and learn why they are called linear.
Click to graph the equation $y=x$ on the grid to the left. If there are any points that aren’t on the line, you have made a mistake in the table. Correct any mistakes you find so that all of the points are on the line.
Click to look at the graphs of $y_1=x$ and $y=x+2$. Correct any mistakes you have made in the table so that all of the blue points are on the blue line.
Click to see the graphs of $y_1=x$, $y_2=x+2$, and $y=x-2$. Correct any mistakes you have made in the table so that all of the green points are on the green line.
This is why the equations $y_1=x$, $y_2=x+2$, and $y=x-2$ are called linear equations: because their graphs are lines.
For each of the three equations we have graphed, find the point where that equation’s graph crosses the $y$-axis (the vertical axis with the arrow at the top). What are the $(x,y)$ coordinates of that point for
The point where a line crosses the vertical axis or $y$-axis is commonly called the $y$-intercept of the line.
The blue line is the graph of $y_1=x+4$, the red line is the graph of $y_2=x$, and the green line is the graph of $y_3=x-4$. Use the slider in the lower left portion of your screen to change the value of $b$ in the equation $y=x+b$ (the purple line).
Use the slider to change the value of $b$ and complete the table below. The equation for $y$ is shown below the grid.
The $y$-axis is the place where $x=0$. So you can also find the $y$-intercept of a line algebraically: by setting $x=0$ in the equation for that line.
Each row of this table gives an equation for a line. By setting $x$ to $0$ in that equation, find the $y$-intercept of that line.
Based on these last two questions, you can see that:
The $y$-intercept of the line $y=x+b$ is the point $(0, b)$.