Math Problem Statement
Find the equation of the linear function represented by the table below in slope-intercept form. Table: x = [1, 2, 3, 4], y = [1, 4, 7, 10].
Solution
Let's analyze the table and find the equation of the linear function in slope-intercept form.
The table given is:
x & y \\ \hline 1 & 1 \\ 2 & 4 \\ 3 & 7 \\ 4 & 10 \\ \end{array}$$ We need to find the equation in the form $$y = mx + b$$, where: - $$m$$ is the slope. - $$b$$ is the y-intercept. ### Step 1: Calculate the slope ($$m$$) The slope formula for two points $$(x_1, y_1)$$ and $$(x_2, y_2)$$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Using the first two points (1, 1) and (2, 4): $$m = \frac{4 - 1}{2 - 1} = \frac{3}{1} = 3$$ So, the slope $$m = 3$$. ### Step 2: Find the y-intercept ($$b$$) Now that we know the slope, we can use one of the points (say $$(1, 1)$$) to find the y-intercept. Plugging into the equation $$y = mx + b$$: $$1 = 3(1) + b$$ $$1 = 3 + b \quad \Rightarrow \quad b = 1 - 3 = -2$$ ### Step 3: Write the equation The equation of the linear function is: $$y = 3x - 2$$ If you have any questions or need more details, feel free to ask! --- Here are 5 related questions you might find helpful: 1. How do you calculate the slope between two points in general? 2. What is the significance of the y-intercept in a linear equation? 3. How can we determine if a function is linear from a table of values? 4. What happens to the slope if the points are reversed in the slope formula? 5. Can you graph this linear function to verify the solution? **Tip:** Always check that the slope is consistent between multiple points in the table to confirm linearity.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Linear equation: y = mx + b
Theorems
Linear equation slope-intercept form
Suitable Grade Level
Grades 6-8