Question

what is an equation of the line whose graph is shown?
multiple choice 4 points
in the accompanying diagram, which is an equation of line $ell$?

Explanation:

Step1: Recall line - equation forms

The general form of a linear equation is $y = mx + b$ (slope - intercept form), where $m$ is the slope and $b$ is the y - intercept. For a vertical line, the equation is of the form $x = a$, and for a horizontal line, the equation is of the form $y=a$.

Step2: Analyze the first graph

The line in the first graph passes through the origin $(0,0)$ and has a slope of 1 (since for every 1 unit increase in $x$, there is a 1 unit increase in $y$). Using the slope - intercept form $y=mx + b$ with $m = 1$ and $b = 0$, the equation is $y=x$.

Step3: Analyze the second graph

The line $\ell$ in the second graph is a vertical line passing through $x = 3$. The equation of a vertical line is of the form $x=a$, where $a$ is the x - coordinate of any point on the line. So the equation of line $\ell$ is $x = 3$.

Answer:

1. A. $y=x$
2. B. $x = 3$