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 $\frac{7}{4}$.

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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!