Question

How do you find the slope of a line $2y = 8x - 3$ ?

Answer 1

Hint: When you’re asked to find the slope of the line for a given equation, it can be really easy if the line is already in $y$ equals $mx$ plus $b$ form. If you remember when $y$ is all by itself and we have an equation solves for $y$, the slope is just the coefficient for $x$, so if I can take this line and solve for $y$,so that $y$ is isolated, then my slope numbers are going to jump out on me. It’s going to be the coefficient of $x$.

Complete step-by-step solution:
The slope-intercept form is
$y = mx + b$
where $m$ is the slope and $b$ is the $y$ -intercept.

Now from the given equation
$ \Rightarrow 2y = 8x - 3$
Divide each term by $2$ and simplify the above equation, we get
$ \Rightarrow \dfrac{{2y}}{2} = \dfrac{{8x}}{2} - \dfrac{3}{2}$
The equation becomes after canceling the common factors
$ \Rightarrow y = 4x - \dfrac{3}{2}$
Now the equation is in the slope intercept form
Therefore by equating them we found that
$m = 4$

The slope of the given equation $2y = 8x - 3$ is $4$

Note: Slope simply as the "rate of change" of a graph if you make the variable $x$ bigger, at what rate does $y$ change.
That is a way to see slope as a cause and an effect event. Use slope to determine how steep, and in what direction (upward or downward), a line goes. Finding the slope of a line is easy, as long as you have or can set up a linear equation.
The slope of a line is a measure of how fast it is changing. This can be for a straight line where the slope tells you exactly how far up (positive slope) or down (negative slope) a line goes while it goes how far across. Slope can also be used for a line tangent to a curve. Or, it can be for a curved line when doing Calculus, where slope is also known as the "derivative" of a function .This method works if and only if:
There are no exponents on the variables
There are only two variables, neither of which are fractions.
The equation can be simplified to the form , where $m$ and $b$ are constants.