Question

which graph matches the equation $y=-\frac{1}{2}x - 1$

Explanation:

Step1: Analyze the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{1}{2}x - 1\), the slope \(m =-\frac{1}{2}\) (negative, so the line should be decreasing from left to right) and the y - intercept \(b=- 1\) (the line crosses the y - axis at \((0,-1)\)).

Step2: Evaluate the graphs

• The second and third graphs have positive slopes (lines increasing from left to right), so they can be eliminated.
• The fourth graph has a y - intercept at \((0,0)\), not \((0, - 1)\), so it can be eliminated.
• The first graph has a negative slope (decreasing from left to right) and a y - intercept at \((0,-1)\), which matches the equation \(y =-\frac{1}{2}x-1\).

Answer:

The first graph (the left - most graph among the four given graphs)