Math Problem Statement
Solution
The graph shows the linear function passing through the points and . To determine the zero of the function, we need to find the x-intercept, which is the value of when .
Let's start by finding the equation of the line in slope-intercept form .
Step 1: Calculate the slope
The formula for slope between two points and is:
Substituting the given points and :
So, the slope .
Step 2: Use point-slope form to find the equation of the line
Now, using the point-slope form of the equation of a line, , we can substitute one of the points, say , and the slope :
Simplifying:
Step 3: Find the zero of the function
To find the zero, set and solve for :
Add 9 to both sides:
Now, divide by 1.5:
Thus, the zero of the function is .
Do you need further clarification or more details?
Here are 5 related questions to explore further:
- How can we verify that the equation of the line is correct using both points?
- What is the significance of the slope in a linear function?
- How do we interpret the y-intercept of the function?
- Can you find the zero of a quadratic function using a similar method?
- What is the connection between the slope and the steepness of a line?
Tip: When calculating the slope, always double-check the signs of your coordinates to ensure accuracy!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10