Math Problem Statement
Solution
To write the equation of the line in the graph, we can use the slope-intercept form of the equation of a line:
where:
- is the slope of the line,
- is the y-intercept (the point where the line crosses the y-axis).
Step 1: Find the slope
The slope of a line is the change in divided by the change in , which is calculated as:
Looking at the graph, I will select two points on the line:
- Point 1:
- Point 2:
Now calculate the slope:
So, the slope is 2.
Step 2: Find the y-intercept
The y-intercept is the point where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at .
Thus, .
Final Equation
Now that we know and , the equation of the line is:
Would you like further details or have any questions?
Here are some related questions:
- How do you calculate the slope of a line from its graph?
- What is the significance of the y-intercept in a linear equation?
- How do you convert from slope-intercept form to standard form?
- What does it mean if a line has a slope of zero?
- How can you determine if two lines are parallel based on their equations?
Tip: Always check if the line crosses the y-axis at zero, as that simplifies your equation greatly by eliminating the constant .
Ask a new question for Free
By Image
Drop file here or Click Here to upload
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 Theorem
Suitable Grade Level
Grades 8-10