To graph the equation $x - 3y = 15$ using slope-intercept form, we first need to rearrange the equation so that $y$ is by itself on one side. The slope-intercept form looks like this:
$$y = mx + b$$
where:
* $m$ is the slope
* $b$ is the y-intercept (the point where the line crosses the vertical y-axis)
Step 1: Isolate $y$
Start with the original equation:
$$x - 3y = 15$$
Subtract $x$ from both sides to move it to the right:
$$-3y = -x + 15$$
Divide every term by $-3$ to get $y$ alone:
$$y = \frac{-x}{-3} + \frac{15}{-3}$$
Simplify the fractions:
$$y = \frac{1}{3}x - 5$$
Now the equation is in slope-intercept form ($y = mx + b$).
* Slope ($m$) = $\frac{1}{3}$
* Y-intercept ($b$) = $-5$
Step 2: Plot the Y-intercept
The y-intercept is $-5$. This means the line crosses the y-axis at the point $(0, -5)$.
* Start at the origin $(0,0)$.
* Count down 5 units on the vertical axis.
* Place a dot at $(0, -5)$.
Step 3: Use the Slope to find another point
The slope is $\frac{1}{3}$. Remember "rise over run":
*
Rise (numerator): Go up 1 unit.
*
Run (denominator): Go right 3 units.
Starting from your dot at $(0, -5)$:
1. Move
up 1 square.
2. Move
right 3 squares.
3. Place a new dot at this location. This point is $(3, -4)$.
*(You can repeat this step to find more points if you want to be sure, e.g., go up 1 and right 3 again to get to $(6, -3)$).*
Step 4: Draw the Line
Use a ruler to draw a straight line through the points you plotted. Extend the line across the grid and add arrows at both ends to show it goes on forever.
Final Answer:
The graph is a straight line passing through the y-intercept
(0, -5) with a slope of
1/3 (rising 1 unit for every 3 units moved to the right). Key points on the line include
(0, -5),
(3, -4), and
(15, 0).
Parent Tip: Review the logic above to help your child master the concept of graphing linear equations review.
