Question

How do you write $ - 3x + 2y = 7$ in slope-intercept form $?$ what is the slope and $y$-intercept $?$

Answer 1

Hint: In this question, we are going to write the given equation in slope-intercept form.
First we are going to find the equation of a line by rewriting the given equation.
From the equation of a line, we can easily find the slope and $y$-intercept of a line.
Hence, we can get the required result.

Formula used: Every straight line can be represented by an equation:
$y = mx + b$
The equation of any straight line, called a linear equation, can be written as $y = mx + b$
Where $m$ is the slope of the line and $b$ is the $y$-intercept.
$y = Y$ coordinate
$x = X$ coordinate

Complete step-by-step solution:
In this question, we are going to write the given equation in slope-intercept form.
The given equation is $ - 3x + 2y = 7$
The given linear equation is not in the slope - intercept form
First we are going to find the equation of a line by rewriting the given equation.
$ \Rightarrow 2y = 7 + 3x$
On rewriting we get
$ \Rightarrow y = \dfrac{{7 + 3x}}{2}$
On spiting we get,
$ \Rightarrow y = \dfrac{{3x}}{2} + \dfrac{7}{2}$
This is the required slope-intercept form of the equation.
The equation is of the form $y = mx + b$
Here the slope of the equation is $\dfrac{3}{2}$ and the$y$-intercept of the equation is $\dfrac{7}{2}$
To find the $y$-intercept put $x = 0$in the equation and solve for $y$
$ \Rightarrow y = \dfrac{3}{2}\left( 0 \right) + \dfrac{7}{2}$
$ \Rightarrow y = \dfrac{7}{2}$
The $y$-intercept can also be written as $\left( {0,\dfrac{7}{2}} \right)$

The slope- intercept form of the equation $ - 3x + 2y = 7$ is $y = \dfrac{3}{2}x + \dfrac{7}{2}$ , the slope and $y$-intercept of the equation is $\dfrac{3}{2}$ and $\dfrac{7}{2}$ respectively.

Note: The $y$-intercept of this line is the value of $y$ at the point where the line crosses the $y$-axis.
The slope is the number $m$ that is multiplied on the $x$.
A decreasing linear function results in a graph that slants downward from left to right and has a negative slope.
A constant linear function results in a graph that is a horizontal line.
Analyzing the slope within the context of a problem indicates whether a linear function is increasing, decreasing, or constant.