To determine if the given equation is a linear equation, let's first see if we can rewrite it in standard form.
Ax+ By= CIn this form, A, B, and C are constants and either A or B must be nonzero.
This is the standard form of the given equation. Below we have highlighted how it corresponds to the general standard form.
x-y=-5 ⇔ 1x+( -1)y= -5
When written this way, we can see that A= 1, B= -1, and C= -5. Since this equation can be written in standard form, it is linear.
Extra
Graphing the Function
We are able to 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 4 means that the graph passes through the x-axis at the point ( 4,0).
Finding the y-intercept
Let's use the same concept 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.
