Question

graph the line that has a slope of -3 and includes the point (1, 3). click to select points on the graph.

Explanation:

Step1: Recall point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m=-3$ and $(x_1,y_1)=(1,3)$. Substitute these values into the formula:
$y - 3=-3(x - 1)$

Step2: Simplify the equation

Expand the right - hand side: $y - 3=-3x+3$. Then, add 3 to both sides of the equation to get the slope - intercept form ($y=mx + b$):
$y=-3x + 3+3$
$y=-3x+6$

Step3: Find two points on the line

We already know the point $(1,3)$ is on the line. Let's find another point. When $x = 0$, substitute $x = 0$ into $y=-3x + 6$:
$y=-3(0)+6=6$. So the point $(0,6)$ is on the line. When $x = 2$, $y=-3(2)+6=-6 + 6=0$. So the point $(2,0)$ is on the line. To graph the line, plot the points $(1,3)$, $(0,6)$, $(2,0)$ (or any two of these points) and draw a straight line through them.

Answer:

To graph the line:

1. Plot the point $(1,3)$ (given point).
2. Use the slope $m=-3=\frac{\text{rise}}{\text{run}}=\frac{- 3}{1}$. From the point $(1,3)$, move 1 unit to the right (increase $x$ by 1) and 3 units down (decrease $y$ by 3) to get the point $(2,0)$. Or move 1 unit to the left (decrease $x$ by 1) and 3 units up (increase $y$ by 3) to get the point $(0,6)$.
3. Draw a straight line through the plotted points.