The equation given is a linear equation in two variables, \(x\) and \(y\). We can analyze and solve it in several ways:

### 1. Solving for One Variable
If you want to express one variable in terms of the other, you can solve for either \(x\) or \(y\).

**Solving for \(x\):**
\[
3x + 4y = 7
\]
\[
3x = 7 - 4y
\]
\[
x = \frac{7 - 4y}{3}
\]

**Solving for \(y\):**
\[
3x + 4y = 7
\]
\[
4y = 7 - 3x
\]
\[
y = \frac{7 - 3x}{4}
\]

### 2. Finding the Intercepts
To find where the line intersects the axes:

- **x-intercept:** Set \(y = 0\).
  \[
  3x + 4(0) = 7 \implies x = \frac{7}{3}
  \]

- **y-intercept:** Set \(x = 0\).
  \[
  3(0) + 4y = 7 \implies y = \frac{7}{4}
  \]

So, the intercepts are \((\frac{7}{3}, 0)\) and \((0, \frac{7}{4})\).

### 3. Graphing the Equation
The equation represents a straight line. You can plot the points found (intercepts) and draw a line through them.

### 4. General Form
The equation \(3x + 4y = 7\) is already in the standard linear form \(Ax + By = C\), where \(A = 3\), \(B = 4\), and \(C = 7\).

### 5. Slope-Intercept Form
To find the slope and y-intercept, rewrite the equation in the form \(y = mx + b\):

\[
4y = -3x + 7 \implies y = -\frac{3}{4}x + \frac{7}{4}
\]

Here, the slope (\(m\)) is \(-\frac{3}{4}\) and the y-intercept (\(b\)) is \(\frac{7}{4}\).

---

Would you like more details on any of these methods, or do you have any other questions?

### Related Questions:
1. How do you find the slope of a line between two points?
2. What is the standard form of a linear equation?
3. How do you determine if two lines are parallel or perpendicular?
4. How can we solve a system of linear equations?
5. What are different methods to graph a linear equation?

**Tip:** Understanding different forms of linear equations helps to solve and graph them efficiently!

Explore how to solve the linear equation 3x + 4y = 7 by expressing variables in terms of each other, finding intercepts, and graphing. This detailed guide covers the algebraic steps to rewrite the equation in slope-intercept form and find the x- and y-intercepts. Suitable for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation