Math Problem Statement
Identify the graph that corresponds to the equation y = -4x - 3 from the given options.
Solution
The problem you uploaded shows an equation and multiple graphs (A, B, C, D) with corresponding sets of points. Your task seems to be to identify which graph corresponds to the given linear equation by checking the slope and y-intercept.
The equation is in slope-intercept form , where:
- The slope is .
- The y-intercept is (the point where the line crosses the y-axis, i.e., ).
Analyzing the equation:
- The slope means for every increase of 1 unit in , decreases by 4 units.
- The line crosses the y-axis at .
Let's evaluate each graph:
- Graph A passes through , which matches the y-intercept.
- We can check if the slope matches by examining the rise/run between points. If we move from to another point like , the change in is , and the change in is . The slope is indeed .
Thus, Graph A matches the equation .
Would you like more details or have further questions?
Here are 5 related questions:
- What does the slope represent in a linear equation?
- How do you determine the slope from a graph?
- What is the significance of the y-intercept?
- Can you find the equation of a line given two points on the line?
- How do parallel and perpendicular lines relate to their slopes?
Tip: Always verify both the slope and y-intercept when matching equations to graphs.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing
Slope-Intercept Form
Formulas
y = mx + b (Slope-Intercept Form)
Slope Formula: (y2 - y1) / (x2 - x1)
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 8-10