Question

How do you write $5x - 3y = 24$ in slope-intercept form?

Answer 1

Hint: Convert the equation to slope-intercept form by solving for $y$ .
The slope intercept form of a line is given by
$y = mx + c$
where$m$ is the slope of the line and $b$ is the $y$-intercept of the line or the $y$-coordinate of the point at which the line crosses the $y$-axis.
First transfer $5x$ to the right-hand side of the equation then divide the whole equation by $ - 3$ .

Complete step-by-step solution:
The given equation, $5x - 3y = 24$ is in the standard form of a line.
The slope intercept form of a line is $y = mx + c$ ,where $m$ is the slope of the line and $b$ is the $y$-intercept of the line, or the $y$-coordinate of the point at which the line crosses the $y$-axis.
Subtract $5x$ from each side of the equation,
$5x - 3y - 5x = 24 - 5x$
$ \Rightarrow - 3y = 24 - 5x$
Divide each side of the equation by $ - 3$,
$ \Rightarrow \dfrac{{ - 3y}}{{ - 3}} = \dfrac{{24}}{{ - 3}} - \dfrac{{5x}}{{ - 3}}$
$ \Rightarrow y = \dfrac{{5x}}{3} - 8$
Compare the above equation with the slope intercept form of a line is $y = mx + c$.
Here, $m = \dfrac{5}{3}$ and $b = - 8$ .

The slope intercept form of $5x - 3y = 24$ is $y = \dfrac{{5x}}{3} - 8$.

Note: The linear equation written in the form $y = mx + c$ is in slope-intercept form where:$m$ is the slope, and $b$ is the $y$-intercept.
The slope $m$ measures how steep the line is with respect to the horizontal. Given two points $\left( {{x_1},{y_1}} \right)$ and $\left( {{x_2},{y_2}} \right)$ found in the line, the slope is computed as
$m = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$