Math Problem Statement
Solution
To find the x-intercept of the graph of the linear function shown in the table, we first need to establish the equation of the line by determining the slope and y-intercept, then solve for the x-intercept.
Step 1: Find the slope (m)
The slope of a line is given by: We can take any two points from the table. Let's use the points (-3, 18) and (-2, 16): Thus, the slope is .
Step 2: Use the point-slope form to find the equation of the line
We can now use the point-slope form of the equation of a line, which is: Substituting and the point (-3, 18): Simplifying: So the equation of the line is .
Step 3: Find the x-intercept
The x-intercept occurs when . Substituting into the equation: Solving for :
Thus, the x-intercept is .
The correct answer is 6.
Would you like further explanation or details?
Here are five related questions to expand your understanding:
- What is the significance of the slope in a linear function?
- How can you quickly identify the y-intercept from the equation of a line?
- How do changes in slope affect the steepness of a line?
- What are the differences between x-intercepts and y-intercepts?
- How would you find the y-intercept using the points in the table?
Tip: Remember, the x-intercept is where the line crosses the x-axis, and at this point, .
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
X-Intercept
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Linear equation: y = mx + b
Theorems
Linear Equation
Suitable Grade Level
Grades 8-10