Math Problem Statement
Solution
To write the equation of the line shown in the image in slope-intercept form, we need two pieces of information:
- The slope of the line.
- The y-intercept (the point where the line crosses the y-axis).
Step 1: Identify two points on the line
Looking at the graph, the line passes through two clear points:
- Point 1:
- Point 2:
Step 2: Calculate the slope
The slope is calculated using the formula:
Substituting the coordinates of the two points:
Step 3: Determine the y-intercept
To find the y-intercept , we use the slope-intercept form of the line equation:
Substitute the slope and one of the points, say , into the equation:
Simplifying:
Step 4: Write the equation
Now that we have the slope and the y-intercept , the equation of the line is:
This is the equation in slope-intercept form.
Would you like any further details or explanations?
Here are 5 related questions to deepen your understanding:
- How do you calculate the slope if you have two points?
- What does the y-intercept represent in a linear equation?
- How would the equation change if the slope was positive?
- Can you find the equation of a line if the y-intercept is not given but two points are?
- How would you write the equation if it were in point-slope form instead?
Tip: When calculating the slope, always subtract the coordinates in the same order (i.e., always and ) to avoid sign errors.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
y = mx + b
Slope formula m = (y2 - y1) / (x2 - x1)
Theorems
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Suitable Grade Level
Grades 8-10