Question

graph the line with the equation $y = -\frac{1}{2}x - 3$.

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{1}{2}x - 3\), when \(x = 0\), \(y=-3\). So, plot the point \((0,-3)\).

Step2: Use the slope to find another point

The slope \(m =-\frac{1}{2}\). From the point \((0,-3)\), using the slope formula \(m=\frac{\Delta y}{\Delta x}\), if \(\Delta x = 2\) (run), then \(\Delta y=-1\) (rise). So, from \((0,-3)\), move 2 units to the right and 1 unit down. The new point is \((2,-4)\).

Step3: Draw the line

Connect the points \((0,-3)\) and \((2,-4)\) and extend the line in both directions.

Answer:

Plot the point \((0, - 3)\) (y - intercept). Then, using the slope \(m =-\frac{1}{2}\), from \((0,-3)\) move 2 units right and 1 unit down to get \((2,-4)\). Connect these two points and extend to graph the line \(y =-\frac{1}{2}x-3\).