To determine if the given equation is a linear equation, let's first see if we can rewrite it in standard form.
Ax+ By= C
In this form, A, B, and C are constants and either A or B must be nonzero.
We can see that our equation is already in the standard form. Below we have highlighted how it corresponds to the general standard form.
2x+y=4 ⇔ 2x+ 1y= 4
When written this way, we can see that A= 2, B= 1, and C= 4. Since this equation can be written in standard form, it is linear.
We will graph this equation by finding and plotting its intercepts, then connecting them with a line. To find the x- and y-intercepts, we will need to substitute 0 for one variable, solve, then repeat for the other variable.
Finding the x-intercept
Think of the point where the graph of an equation crosses the x-axis. The y-value of that ( x, y) coordinate pair is equal to 0, and the x-value is the x-intercept. To find the x-intercept of the given equation, we should substitute 0 for y and solve for x.
An x-intercept of 2 means that the graph passes through the x-axis at the point ( 2,0).
Finding the y-intercept
Let's use the same method to find the y-intercept. Consider the point where the graph of the equation crosses the y-axis. The x-value of the ( x, y) coordinate pair at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.
