Math Problem Statement
Solution
From the image, the task is to write an equation in slope-intercept form of the line shown on the graph. The slope-intercept form of a line is expressed as:
where is the slope and is the y-intercept.
Let's determine the slope () first. The slope can be calculated by selecting two points on the line and using the formula:
From the graph, we can select the points (1, 3) and (3, 1). Plugging these into the formula:
Next, the y-intercept () is the point where the line crosses the y-axis. Observing the graph, the line crosses the y-axis at . Therefore, .
Combining these, the equation of the line in slope-intercept form is:
Or simply:
Would you like more details on how to find the slope or y-intercept from a graph? Do you have any questions?
- Would you like to see another example of writing an equation from a graph?
- Do you need clarification on how the y-intercept is identified on a graph?
- Are you interested in learning about different forms of linear equations?
- Would you like to know how to check if a point lies on this line?
- Are there other types of equations or graphs you're curious about?
Tip: When choosing points from a graph to calculate the slope, it's often useful to pick points where the line crosses grid lines to ensure accuracy.
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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
Slope-Intercept Form of a Line
Suitable Grade Level
Grade 8-9