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

Answer

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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.

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