Math Problem Statement
Using the gradient intercept method, sketch and make a table of y= 2/3 x -2
Solution
Gradient-Intercept Method for
To sketch the graph and make a table for the line , let's go step by step.
Step 1: Identify the slope (gradient) and the y-intercept.
- Slope (Gradient):
- Y-Intercept: The line crosses the y-axis at , so the intercept is .
Step 2: Plot the y-intercept.
- Start by plotting the point on the graph. This is where the line crosses the y-axis.
Step 3: Use the slope to find additional points.
The slope tells us that for every 3 units you move to the right (increase in ), the -value increases by 2 units. You can also go in the reverse direction (left by 3, down by 2).
- From , move 3 units to the right and 2 units up to get the point .
- You can also go in the reverse direction: from , move 3 units to the left and 2 units down to get the point .
Step 4: Draw the line.
Connect the points , , and with a straight line. This is the graph of the equation .
Step 5: Make a table of values.
Here’s a table of values to correspond with the line:
\hline x & y \\ \hline -6 & -6 \\ -3 & -4 \\ 0 & -2 \\ 3 & 0 \\ 6 & 2 \\ \hline \end{array}$$ #### Visualization: You can sketch the graph based on the points in the table. It will be a straight line, sloping upwards with a gentle rise (since the slope is less than 1). Would you like any further clarification on how this method works, or do you have any questions? --- Here are 5 follow-up questions related to this topic: 1. How do you find the slope if the equation is not in slope-intercept form? 2. What happens to the graph when the slope is negative? 3. Can you determine the x-intercept algebraically from the equation $$y = \frac{2}{3}x - 2$$? 4. How do you interpret the slope in real-world problems? 5. What changes would occur if the y-intercept were positive instead? **Tip:** Always check your table values with the original equation to ensure accuracy when sketching graphs!Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9