Question

graph the function $f(x) = -x + 8$.

Explanation:

Step1: Identify the y - intercept

The function is in the form \(y = mx + b\), where \(b\) is the y - intercept. For \(f(x)=-x + 8\), when \(x = 0\), \(y=f(0)=-0 + 8=8\). So the y - intercept is \((0,8)\). We plot this point on the graph (on the y - axis at \(y = 8\)).

Step2: Identify the slope

The slope \(m\) of the line \(y=-x + 8\) is \(- 1\), which can be written as \(\frac{-1}{1}\). The slope is the rise over run, so from the y - intercept \((0,8)\), we can go down 1 unit (because the rise is - 1) and then right 1 unit (run is 1) to get another point. For example, when \(x = 1\), \(y=f(1)=-1 + 8 = 7\), so the point is \((1,7)\). We can also find the x - intercept by setting \(y = 0\): \(0=-x + 8\), which gives \(x = 8\). So the x - intercept is \((8,0)\).

Step3: Draw the line

Using the two points (for example, \((0,8)\) and \((8,0)\) or \((0,8)\) and \((1,7)\)), we draw a straight line passing through these points. The line should have a negative slope (going down from left to right) and pass through the y - intercept at \((0,8)\) and x - intercept at \((8,0)\).

(Note: Since this is a graphing problem, the final answer is the graph of the line with y - intercept \((0,8)\) and x - intercept \((8,0)\) and a slope of \(-1\).)

Answer:

The graph of \(f(x)=-x + 8\) is a straight line passing through the points \((0,8)\) (y - intercept) and \((8,0)\) (x - intercept) with a slope of \(-1\). (To draw it, plot these two points on the given coordinate plane and draw a straight line through them.)