Math Problem Statement
Solution
Let's go through each question in the images:
Question 1 (Image 1: Function Equation for the Graph)
The blue line on the graph passes through the point , meaning the y-intercept is 2. The slope can be determined by picking two points along the line. From the graph, the line seems to go through and , which gives a slope (rise over run) of: Thus, the equation of the line is: So, the correct choice is: f(x) = x + 2 or y = x + 2.
Question 2 (Image 2: Scale of the y-axis)
The graph provided in this image shows that at , the corresponding -value is approximately 15. The y-axis seems to be scaled so that each grid line counts by 1.5 units (since from 0 to 15, there are 10 grid lines, each counting 1.5).
Thus, the correct answer is: 1.5.
Let me know if you'd like further details or clarifications on these problems!
Here are five related questions for practice:
- What is the slope of a line passing through points and ?
- How do you determine the slope of a line given its equation in standard form?
- If a line has a slope of and a y-intercept of , what is the equation of the line?
- What does the slope of a line tell you about the direction of the line on a graph?
- How can you find the equation of a line given a point on the line and its slope?
Tip: To find the slope of a line on a graph, pick two points on the line and apply the formula .
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing Functions
Slopes and Intercepts
Scaling on Graphs
Formulas
Slope formula (m = (y2 - y1) / (x2 - x1))
Linear equation (y = mx + b)
Theorems
Slope-Intercept Theorem
Suitable Grade Level
Grades 7-9
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