Question

Use a table of values to graph the equation. Label the x-intercept and the y-intercept. $$ y=-x+8 $$

Short answer

Table values would be (-2,10), (0,8), and (2,6). The y-intercept is (0, 8) and x-intercept is (8, 0).

Step-by-step solution

Understand the Equation

Let's look at the equation \(y = -x + 8\). This is a linear equation in slope-intercept form \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept. The slope of this line is -1 (the coefficient of \(x\)) and the y-intercept is 8. This would mean that for every unit increase in \(x\), \(y\) decreases by 1 unit, starting from the point (0, 8).

Create the Table

Next step is to create a table of values that will give the points to plot on the graph. Choose several values for \(x\) and compute for \(y\) using the equation \(y = -x + 8\). For example, the values for \(x\) can be -2, 0, and 2.

Compute for Y and Complete the Table

Compute for \(y\) using the selected values for \(x\) and the equation \(y = -x + 8\). For \(x = -2\), \(y = 10\), for \(x = 0\), \(y = 8\), and for \(x = 2\), \(y = 6\).

Plot the Points and Draw the Line

Next, plot the points (-2, 10), (0, 8), and (2, 6) on the graph. Draw a line passing through these points. This line represents the equation \(y = -x + 8\).

Label the X and Y-Intercepts

The y-intercept is the point where the line crosses the y-axis and for this equation, it's (0, 8). The x-intercept is the point where the line crosses the x-axis, and you can find this by setting y=0 in the equation and solving for x: 0 = -x + 8, so \(x = 8\). So, the x-intercept is (8, 0). Label these points on the graph.