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The equation
2y-7x=5 is graphed in the
xy-plane. What is the slope of the line?

The equation $2 y-7 x=5$ is graphed in the $x y$ -plane. What is the slope of the line?

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Standard form: find x- and y-intercepts

Full solution

Q. The equation

2 y-7 x=5

is graphed in the

x y

-plane. What is the slope of the line?

Identify Given Equation and Goal: Identify the given equation and the goal. $\newline$ The given equation is $2y - 7x = 5$ , and we need to find the slope of the line it represents.
Rewrite in Slope-Intercept Form: Rewrite the equation in slope-intercept form, $y = mx + b$ , where $m$ is the slope. $\newline$ Start by isolating $y$ on one side of the equation: $2y = 7x + 5$ .
Divide to Solve for y: Divide every term by $2$ to solve for $y$ : $y = \frac{7}{2}x + \frac{5}{2}$ . This puts the equation in the form $y = mx + b$ , where $m$ is the slope.
Identify the Slope: Identify the slope from the equation $y = \frac{7}{2}x + \frac{5}{2}$ . $\newline$ The slope ( $m$ ) is $\frac{7}{2}$ .

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