Question

graph the line with slope $-\frac{1}{2}$ passing through the point $(4, 2)$.

Explanation:

Step1: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(4,2)\) and \(m =-\frac{1}{2}\).
Substitute the values: \(y - 2=-\frac{1}{2}(x - 4)\).

Step2: Simplify the equation

$$
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$$

Step3: Find another point

Let \(x = 0\), then \(y=-\frac{1}{2}(0)+4 = 4\), so we have the point \((0,4)\).
Let \(x = 2\), then \(y=-\frac{1}{2}(2)+4=-1 + 4=3\), so we have the point \((2,3)\).

Step4: Plot the points and draw the line

Plot the point \((4,2)\), \((0,4)\) and \((2,3)\) on the coordinate plane. Then use a straight - edge to draw a line passing through these points.

Answer:

Plot the point \((4,2)\). From \((4,2)\), use the slope \(m =-\frac{1}{2}\) (which means for every 2 units we move to the right, we move 1 unit down; or for every 2 units we move to the left, we move 1 unit up). Another way is to use the equation \(y =-\frac{1}{2}x + 4\) to find more points (e.g., \((0,4)\)) and then draw the line passing through the relevant points.