Question

use the following key features to graph the line:
x-intercept: (3,0)
y-intercept: (0,6)
slope: m = -2

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. We know that $m=- 2$ and $b = 6$ (since the $y$-intercept is $(0,6)$), so the equation of the line is $y=-2x + 6$.

Step2: Plot the intercepts

We are given the $x$-intercept $(3,0)$ and the $y$-intercept $(0,6)$. First, mark the point $(0,6)$ on the $y$-axis and the point $(3,0)$ on the $x$-axis.

Step3: Use the slope to find another point (optional for graphing)

The slope $m=-2=\frac{-2}{1}=\frac{\text{rise}}{\text{run}}$. Starting from the $y$-intercept $(0,6)$, if we move down 2 units (rise $=- 2$) and then move right 1 unit (run $ = 1$), we get the point $(0 + 1,6-2)=(1,4)$. We can also verify using the equation: when $x = 1$, $y=-2(1)+6=4$, which matches.

Step4: Draw the line

Draw a straight line passing through the points $(0,6)$ and $(3,0)$ (and other points we found like $(1,4)$ if needed). The line should connect these points and extend in both directions.

To graph the line:

1. Mark the point $(0,6)$ (y - intercept) on the y - axis.
2. Mark the point $(3,0)$ (x - intercept) on the x - axis.
3. Draw a straight line passing through these two points. The line has a slope of - 2, which means it is a decreasing line (as $x$ increases, $y$ decreases) and for every 1 unit increase in $x$, $y$ decreases by 2 units.

Answer:

The line is graphed by plotting the points $(0,6)$ (y - intercept) and $(3,0)$ (x - intercept) and drawing a straight line through them (with a slope of - 2, confirming the line's steepness and direction).