Question

graph the function $h(x)=-dfrac{1}{2}x + 2$.

Explanation:

Step1: Find the y - intercept

The function is in the form \(y = mx + b\), where \(b\) is the y - intercept. For \(h(x)=-\frac{1}{2}x + 2\), when \(x = 0\), \(h(0)=-\frac{1}{2}(0)+2=2\). So the point \((0,2)\) is on the graph.

Step2: Find another point using the slope

The slope \(m =-\frac{1}{2}\). From the point \((0,2)\), using the slope formula \(m=\frac{\Delta y}{\Delta x}\). If \(\Delta x = 2\), then \(\Delta y=-\frac{1}{2}\times2=-1\). So another point is \((0 + 2,2-1)=(2,1)\)

Step3: Draw the line

Plot the points \((0,2)\) and \((2,1)\) on the coordinate plane and draw a straight line passing through them.

Answer:

Plot the points \((0,2)\) and \((2,1)\) and draw a straight line through them to graph \(h(x)=-\frac{1}{2}x + 2\)