Question

How do you find the slope given $4x + 3y = 24$?

Answer 1

Hint: First we know that the slope-intercept form. Proportional linear functions can be written form $y = mx + b$, where $m$ is the slope of the line. Non-proportional linear functions can be written in the form $y = mx + b$,$b \ne 0$
We find $m$.
We just use the substitute, addition and division.
Finally we get the slope in the given linear equation.

Complete step-by-step solution:
The given equation is: $4x + 3y = 24$
Rearrange the equation to follow the slope-intercept form
Once your equation is in slope-intercept form:
$y = mx + b$
The coefficient of $x$($m$) is the slope. The constant of ($b$) is the $y$-intercept at $(0,b)$
Isolate $y$ and simplify, hence we get
$4x + 3y = 24$
$\Rightarrow$$3y = - 4x + 24$
Divide by $3$ on both sides, hence we get
$\Rightarrow$$\dfrac{{\not{3}}}{{\not{3}}}y = \dfrac{{ - 4x + 24}}{3}$
$\Rightarrow$$y = \dfrac{{ - 4x + 24}}{3}$
Now we divide into individual, hence we get
$\Rightarrow$$y = \dfrac{{ - 4}}{3}x + \dfrac{{24}}{3}$
Divide $24$ by $3$, hence we get
$\Rightarrow$$y = \dfrac{{ - 4}}{3}x + 8$
Now the slope-intercept form is$y = mx + b$
Hence the $m$ is $ - \dfrac{4}{3}$

So, the slope is $ - \dfrac{4}{3}$

Note: The slope-intercept form is probably the most frequently used way to express the equation of a line. Proportional linear functions can be written form $y = mx + b$, where $m$ is the slope of the line. Non-proportional linear functions can be written in the form $y = mx + b$,$b \ne 0$. This is called the slope-intercept form of a straight line because $m$ is the slope $b$ is the $y$-intercept.
The conditions are:
When $b = 0$ and $m \ne 0$, the line passes through the origin and its equation is $y = mx$.
When $b = 0$ and $m = 0$, the coincides with the $x$-axis and its equation is $y = 0$
When $b \ne 0$ and $m = 0$, the line is parallel to the $x$-axis and its equation is $y = b$.