Math Problem Statement
Solution
To find the equation of the line in slope-intercept form (which is , where is the slope and is the y-intercept), we need to determine the slope and the y-intercept.
Step 1: Identify two points on the line.
From the image, it appears that two points on the line are:
Step 2: Calculate the slope.
The slope is calculated by the formula: Using the points and :
Step 3: Determine the y-intercept.
The slope-intercept form is . We already know the slope .
Now, substitute one of the points (let's use ) into the equation to solve for :
Step 4: Write the equation.
Thus, the equation of the line in slope-intercept form is:
Would you like more details on this solution, or do you have any questions?
Here are 5 related questions:
- How do you find the slope if you are given only two points?
- What are the different forms of the equation of a line?
- How can you graph a line given its slope-intercept form equation?
- What does the slope represent geometrically?
- How can you convert the slope-intercept form to the standard form?
Tip: The y-intercept is the point where the line crosses the y-axis, and it occurs when .
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Slope-Intercept form: y = mx + b
Theorems
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Suitable Grade Level
Grades 8-10
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