Question

3 y = x - 3

Explanation:

Step1: Identify slope-intercept form

The equation $y = x - 3$ follows the slope-intercept form $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

Step2: Extract y-intercept

From $y = x - 3$, the y-intercept $b = -3$. This means the line crosses the y-axis at the point $(0, -3)$.

Step3: Extract slope

The slope $m = 1$, which can be written as $\frac{1}{1}$. This means for every 1 unit increase in $x$, $y$ increases by 1 unit.

Step4: Plot additional points

Using the slope, from the y-intercept $(0, -3)$:

• Move 1 unit right and 1 unit up to get $(1, -2)$
• Move 1 unit right and 1 unit up again to get $(2, -1)$
• Move 1 unit left and 1 unit down from $(0, -3)$ to get $(-1, -4)$

Step5: Draw the line

Connect the plotted points $(0, -3)$, $(1, -2)$, $(2, -1)$, $(-1, -4)$ with a straight line, extending it in both directions.

Answer:

The line $y = x - 3$ is a straight line with a slope of 1, y-intercept at $(0, -3)$, passing through points such as $(1, -2)$, $(2, -1)$, and $(-1, -4)$. When graphed, it rises from left to right across the coordinate plane.