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What is the slope of 3x - 7y = 11?

Last updated date: 16th Jul 2024
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Hint: In order to determine slope, solve for $y$ to convert the equation to slope-intercept form. The equation of a line in slope-intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. Arrange the given equation in the form of slope-intercept using the slope-intercept form rearrange the given equation as the form of slope. In this problem we have to find the intercept of $y$.
Formula used: linear equation in standard form is $Ax + By = C$
Slope-intercept form of a linear equation is
$y = mx + b$
$y - y$-coordinate
$m$-slope
$x - x$-coordinate
$b - y$-intercept

Complete step-by-step solution:
The given equation is $3x - 7y = 11$
It is a linear equation in standard form
$Ax + By = C$
In order to determine the slope, solve for $y$ to convert the equation to slope-intercept form.
We know that the slope-intercept form in slope intercept form
$y = mx + b$ ………………………….$(1)$
Where, $m$ is the slope and $b$ is the $y$-intercept.
Now we have to arrange the equation in the form of slope intercept form.
$3x - 7y = 11$
Subtract $3x$ from both sides of the equation, we have,
$3x - 7y - 3x = 11 - 3x$
Now, cancel the term $3x$ which have the same value and different sign,
Therefore we have
$- 7y = 11 - 3x$
We have to solve the equation for $y$ to convert the equation. So divide $m$ by both sides of the equation. We have,
$\dfrac{{ - 7y}}{{ - 7}} = \dfrac{{ - 3}}{-7}x + \dfrac{{11}}{{ - 7}}$
$y = \dfrac{3}{7}x - \dfrac{{11}}{7}$ ………………………..$(2)$
Compare this equation $(2)$ with the equation $(1)$ we have,
The slope of the line is $\dfrac{3}{7}$.

Note: Slope is calculated by finding the ratio of the vertical change to the horizontal change between any distinct on a line. Slope intercept: The slope $m$ represents the steepness of a line. The slope of the line is also termed as gradient, sometimes.