Exercise 41 Page 335

We will graph this equation by finding and plotting its intercepts. Then, we will connect them with a line. To find the x- and y-intercepts, we will need to substitute 0 for one variable and solve. After that, 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 coordinate pair ( x, y) 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. Then, solve for x.

An x-intercept of 8 means that the graph passes through the x-axis at the point ( 8,0).

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 coordinate pair ( x, y) at the y-intercept is 0. Therefore, substituting 0 for x will give us the y-intercept.

x+y=8

Substitute

x= 0

0+y=8

AddTerms

Add terms

y=8

A y-intercept of 8 means that the graph passes through the y-axis at the point (0, 8).

Graphing the Equation

We can now graph the equation by plotting the intercepts and connecting them with a line.