Math Problem Statement
Solution
The equation given is , which is a linear equation with a slope of -2 and a y-intercept of 0. This means that the graph is a straight line passing through the origin (0, 0), and the slope tells us that for every 1 unit increase in , decreases by 2 units.
Here’s how to plot the line on the graph:
- Start at the origin (0, 0), since there is no y-intercept term (i.e., the constant term is 0).
- Use the slope to find the next point. The slope can be interpreted as "down 2 units for every 1 unit to the right." So from (0, 0), move 1 unit to the right (to ) and then 2 units down (to ). This gives the point (1, -2).
- You can also move to the left. From the origin, move 1 unit to the left (to ) and then 2 units up (to ). This gives the point (-1, 2).
- Draw a straight line through these points.
The line should pass through points such as (0, 0), (1, -2), and (-1, 2), and continue following the pattern established by the slope.
Would you like more details on how the slope affects the line or have any further questions?
Related questions:
- How do you find the slope of a line given two points?
- How would the graph change if the equation was instead?
- What happens to the graph if you add a y-intercept, such as ?
- How do negative slopes affect the direction of a line compared to positive slopes?
- Can you explain how to calculate the x-intercept of a linear equation?
Tip: The y-intercept is where the line crosses the y-axis, and the x-intercept is where the line crosses the x-axis. For , the y-intercept is at (0, 0).
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Graphing
Formulas
Slope-intercept form: y = mx + b
Theorems
Slope theorem: Slope determines the steepness and direction of a line.
Suitable Grade Level
Grades 8-10