Question

How do you find the slope of \[y = 2x\]?

Answer 1

Hint: 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’.