Question

practice applying the slope - intercept form of an equation. which graph represents the function ( y=\frac{1}{1}x - 2)?

Explanation:

Step1: Identify slope and y-intercept

The slope-intercept form is $y=mx+b$, where $m$ is slope, $b$ is y-intercept. For $y=\frac{1}{1}x-2$, $m=1$, $b=-2$.

Step2: Analyze y-intercept

A y-intercept of $-2$ means the line crosses the y-axis at $(0, -2)$.

Step3: Analyze slope

A slope of $1$ ($\frac{\text{rise}}{\text{run}}=\frac{1}{1}$) means for every 1 unit right, the line rises 1 unit.

Step4: Match to graphs

Only the third graph crosses the y-axis at $(0, -2)$ and has a positive upward slope.

Answer:

The third graph (bottom-left option, crossing y-axis at (0,-2) with positive slope)