Math Problem Statement
Select the correct linear equation that corresponds to the table of values: (x, y) as follows: (0, 3), (3, 15), (7, 31), (10, 43).
Solution
The table provided has pairs of and values as follows:
\hline x & y \\ \hline 0 & 3 \\ 3 & 15 \\ 7 & 31 \\ 10 & 43 \\ \hline \end{array}$$ We are asked to find the linear equation that corresponds to this data. ### Step 1: Find the slope The slope ($$m$$) of a linear equation $$y = mx + b$$ can be calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Let's choose the points $$(0, 3)$$ and $$(3, 15)$$: $$m = \frac{15 - 3}{3 - 0} = \frac{12}{3} = 4$$ So, the slope is $$m = 4$$. ### Step 2: Find the intercept Since one of the points is $$(0, 3)$$, the y-intercept ($$b$$) is $$3$$, because when $$x = 0$$, $$y = 3$$. ### Step 3: Equation of the line Now that we have the slope $$m = 4$$ and the intercept $$b = 3$$, the equation of the line is: $$y = 4x + 3$$ ### Step 4: Select the correct answer The correct equation is $$y = 4x + 3$$, which matches option **D**. Would you like more details or have any questions? Here are some related questions: 1. How do you find the equation of a line using two points? 2. What is the difference between slope-intercept form and point-slope form? 3. Can you explain how to calculate the slope for different pairs of points? 4. How can you determine if a table of values represents a linear function? 5. What are some real-world applications of linear equations? **Tip**: Always check your work by substituting values of $$x$$ into the equation to verify they match the corresponding $$y$$-values in the table.Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Algebra
Formulas
Slope formula: m = (y2 - y1) / (x2 - x1)
Linear equation: y = mx + b
Theorems
Slope-intercept form theorem
Suitable Grade Level
Grades 6-8