Question

match the following linear equations with their corresponding graphs:$y = x$$y = 2x$$y = \frac{1}{2}x$$y = -2x$

Explanation:

Step1: Identify slope of $y=\frac{1}{2}x$

The slope $m=\frac{1}{2}$, a positive, shallow slope (for every +2 in $x$, $y$ increases by +1). This matches the first graph (shallow positive line through origin).

Step2: Identify slope of $y=x$

The slope $m=1$, a positive slope where $x$ and $y$ change equally. This matches the second graph (45-degree positive line through origin).

Step3: Identify slope of $y=2x$

The slope $m=2$, a steep positive slope (for every +1 in $x$, $y$ increases by +2). This matches the third graph (steep positive line through origin).

Step4: Identify slope of $y=-2x$

The slope $m=-2$, a steep negative slope (for every +1 in $x$, $y$ decreases by 2). This matches the fourth graph (steep negative line through origin).

Answer:

• First (leftmost) graph: $y=\frac{1}{2}x$
• Second graph: $y=x$
• Third graph: $y=2x$
• Fourth (bottom right) graph: $y=-2x$