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What is the slope of the line represented by the equation $3x+4y=7$ ?

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Describe the graph of a linear equation

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Q. What is the slope of the line represented by the equation

3x+4y=7

?

Convert to slope-intercept form: Convert the given equation to slope-intercept form $y = mx + b$ . The equation given is $3x + 4y = 7$ . To find the slope, we need to solve for $y$ to get the equation in the form $y = mx + b$ , where $m$ is the slope. Subtract $3x$ from both sides to isolate the $y$ term on one side. $4y = -3x + 7$
Isolate y term: Divide both sides of the equation by $4$ to solve for $y$ . $\newline$ $y = \frac{-3x + 7}{4}$ $\newline$ Simplify the equation by distributing the division across the terms on the right side. $\newline$ $y = \frac{-3}{4}x + \frac{7}{4}$
Solve for $y$ : Identify the slope from the slope-intercept form of the equation. $\newline$ The slope-intercept form of the equation is now $y = \left(-\frac{3}{4}\right)x + \frac{7}{4}$ , where the coefficient of $x$ is the slope ( $m$ ). $\newline$ Therefore, the slope of the line is $-\frac{3}{4}$ .

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