Question

Use a table of values to graph the equation. Label the \(x \text { -intercept and the } y \text { -intercept. (Review } 4.2,4.3)\) $$y=10-x$$

Short answer

The graph of the equation \(y = 10 - x\) is a straight line passing through the points (-1,11), (0,10), (10,0), and (11,-1). The x-intercept is x=10 and the y-intercept is y=10.

Step-by-step solution

Determine the x-intercept and y-intercept

Set y to 0 to find the x-intercept:\n0 = 10 - x\nSolving for x we get that \(x = 10\). Now, set x to 0 to find the y-intercept :\ny = 10 - 0\nwhich gives us that \(y = 10\).

Create a table of values

Choose some values for x and use the equation \(y = 10 - x\) to calculate values of y. Make sure to include the x and y intercepts: So, let x be [-1, 0, 10, 11]. For x = -1, y = 11; for x = 0, y = 10; for x = 10, y = 0; for x = 11, y = -1.

Plot the points and draw the graph

Plot the points from your table on a coordinate plane - (-1,11), (0,10), (10,0), (11,-1). Use a ruler to join the points and extend the line in both directions beyond the plots. Make sure that the line goes through the origin as the intercepts are in the correct places on the x and y axis.