Identify the SLOPE & Y-INTERCEPT. Then graph. x – 3y = 9
The Correct Answer and Explanation is:
Correct Answer:
Slope (m): 1/3
Y-Intercept (b): -3, or the point (0, -3)
Explanation:
To identify the slope and y-intercept of the linear equation x – 3y = 9, the most effective method is to convert it into slope-intercept form, which is written as y = mx + b. In this format, ‘m’ represents the slope of the line, and ‘b’ represents the y-intercept, which is the point where the line crosses the vertical y-axis.
Step 1: Convert the Equation to Slope-Intercept Form (y = mx + b)
- Start with the given equation:
x – 3y = 9 - The goal is to isolate the ‘y’ variable on one side of the equation. First, move the ‘x’ term to the other side by subtracting ‘x’ from both sides:
x – x – 3y = 9 – x
-3y = -x + 9 - Now, solve for ‘y’ by dividing every term in the equation by -3. This will get ‘y’ by itself:
(-3y) / -3 = (-x) / -3 + (9) / -3 - Simplify each term:
y = (1/3)x – 3
Step 2: Identify the Slope and Y-Intercept
Now that the equation is in the y = mx + b format, we can directly identify the components:
- The slope (m) is the coefficient of the ‘x’ term, which is 1/3. A slope of 1/3 means for every 3 units you move to the right on the graph (the “run”), you move 1 unit up (the “rise”).
- The y-intercept (b) is the constant term, which is -3. This means the line crosses the y-axis at the point (0, -3).
Step 3: Graph the Line
- Plot the y-intercept: Begin by placing a point on the y-axis at -3. This is the point (0, -3).
- Use the slope to find a second point: The slope is 1/3 (rise/run). Starting from your first point at (0, -3), “rise” 1 unit up and “run” 3 units to the right.
- From (0, -3), move up 1 unit to (0, -2).
- From (0, -2), move right 3 units to (3, -2).
- This gives you a second point on the line at (3, -2).
- Draw the line: Connect the two points, (0, -3) and (3, -2), with a straight line. Extend this line in both directions with arrows to show it continues infinitely.
This process provides a clear visual representation of the equation x – 3y = 9.
(A graph would be drawn here showing a line passing through the points (0, -3) and (3, -2).)
