Answer
Verified
375.3k+ views
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.
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.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Change the following sentences into negative and interrogative class 10 english CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Application to your principal for the character ce class 8 english CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE