Question

How do you find the slope for $y=2x+4$?

Answer 1

The equation given in the question is a linear equation. So the graph of this equation will be a straight line. For determining the slope of the given equation of line, we need to compare it with the slope – intercept form of a line. The slope – intercept form of a line is given as $y=mx+c$ where $m$ is the slope of the given line, and $c$ is the y – intercept made by the line on the y-axis. On comparing the given equation with this slope – intercept form, we will get the values of the slope and the y – intercept.

Complete step by step answer:
The equation given in the question is
$y=2x+4.......(i)$
As we can see in the above equation, that the dependent variable is $y$ and the independent variable is $x$. Also, the given equation is linear in both $x$ and $y$. So the graph of the given equation is a straight line.
Now, for the determination of the slope of the given line, we need to compare the given equation with the slope – intercept form of a line. We know that the slope intercept of a line is given by
$y=mx+c.......(ii)$
By comparing the equations (i) and (ii), we get
$\Rightarrow m=2$, and
$\Rightarrow c=4$
Thus, the slope of the given line is equal to $2$ and the intercept made by the line on the y-axis is equal to $4$.
Hence, the required value of slope for $y=2x+4$ is equal to $2$.

Note:
For determining the value of the slope of the given line, we could also use differentiation. As we know that the derivative of a curve at a point represents the slope of the tangent to the curve at that point.