Math Problem Statement
Find m and c in 2/3 x + 3/4y = 1 1/2
Solution
We are given the equation:
Our task is to express this in the slope-intercept form, , where is the slope and is the y-intercept.
Step 1: Isolate on one side
We start by isolating the -term on the left-hand side. First, subtract from both sides:
Step 2: Solve for
Next, multiply both sides of the equation by to eliminate the fraction in front of :
Now, distribute the across the terms inside the parentheses:
Simplify each term:
Step 3: Identify and
Now that the equation is in the form :
- The slope
- The y-intercept
Final Answer:
Would you like more details or have any questions?
Here are some related questions to explore:
- How do you find the slope given two points?
- What is the general method for converting a linear equation to slope-intercept form?
- How can you determine the x-intercept from this equation?
- What does the slope of a line represent geometrically?
- How can we verify the solution by graphing?
Tip: When converting to slope-intercept form, always aim to isolate first for clarity!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Slope-Intercept Form
Formulas
Slope-Intercept Form: y = mx + c
Theorems
Conversion to Slope-Intercept Form
Suitable Grade Level
Grades 8-10