Question

How do you find the slope of $y = 2x$?

Answer 1

Here, we will compare the given line with the slope-intercept form to find the slope of the given line. The slope of a line is defined as the value which measures the steepness of the line or the inclination of the line with the $x$ axis.

Formula Used:
By slope-intercept form,$y = mx + c$, where $m$ is the slope of the line and $c$ is the $y$-intercept.

Complete step-by-step answer:
According to the question, the given linear equation in two variables is $y = 2x$, where, $x$and $y$ are the two variables.
Now, as we know, an equation in the slope-intercept form is written in the form of $y = mx + c$.
In this question,
The given equation of the line is $y = 2x$
Comparing this equation with the slope-intercept form $y = mx + c$
We can clearly, say that $m = 2$

Therefore, the slope of this given line is 2.
Hence, this is the required answer.

Additional information:
We know that Slope can be represented in the parametric form and in the point from. A point crossing the $x$-axis is called $x$-intercept, and A point crossing the $y$ -axis is called the $y$-intercept. We know that the horizontal line does not run vertically i.e., ${y_2} - {y_1} = 0$ , so the slope is zero and also the vertical line does not run horizontally i.e., ${x_2} - {x_1} = 0$, the slope is undefined. These slopes are obtained by using the slope of a line using two points formula.

Note:
An equation is called linear equation in two variables if it can be written in the form of $ax + by + c = 0$ where $a,b,c$ are real numbers and $a \ne 0$ , $b \ne 0$ as they are coefficients of $x$ and $y$ respectively. Also, the power of linear equations in two variables will be 1 as it is a ‘linear equation’. Also, as a fun fact, linear equations in two variables can sometimes have infinitely many solutions rather than only one in the case of ‘one variable’.