Math Problem Statement
Solution
The first image shows a graph of a line with three given points: , , and .
To determine the correct equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
Step 1: Find the slope ()
The formula for the slope between two points and is: Using the points and , we can calculate the slope:
Step 2: Find the y-intercept ()
The general slope-intercept form of a line is: We already know the slope , and we can use the point (where ) to find . Substituting into the equation:
Step 3: Write the equation
The equation of the line in slope-intercept form is:
Correct answer:
The correct equation is:
This matches the second option in the second image.
Would you like further clarification or any other help? Here are some related questions you might find interesting:
- How do you find the slope between two points when they are given in a graph?
- What are other forms of linear equations, such as point-slope form and standard form?
- How can you find the equation of a line when you are given only one point and the slope?
- What is the significance of the y-intercept in a linear equation?
- How do you graph a line from its slope-intercept form?
Tip: When solving for the slope, always double-check your calculation to avoid small errors!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Finding Slope and Y-Intercept
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept Form: y = mx + b
Theorems
Equation of a line in slope-intercept form
Suitable Grade Level
Grades 7-9
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