Question

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

Answer 1

Hint: Compare the given equation with the slope intercept form of the equation of a line. Slope intercept form of a line having slope “m” and its y-intercept equals “c” is given as follows, $y = mx + c$.

Complete step by step answer:
In order to find the slope and y intercept of the given equation, let us first understand their meaning.The change of y-value over the change of the x-value is known as slope of a line; it is also called the gradient of a line. And, also known as “Rise over run”.Now, meaning of intercept, Intercept of a line is the point where the line touches $x\;{\text{or}}\;y$ axis.

Coming to the problem, since the given equation of line is written in slope intercept form $y = mx + c$ where $m$ is the slope and $c$ is the y-intercept of the line.We can also write the equation of the line as $y = 2x + 0$.So comparing the equation $y = 2x + 0$ to slope intercept form, we will get
$y = 2x + 0\;{\text{and}}\;y = mx + c \\
\therefore m = 2\;{\text{and}}\;c = 0 \\ $
Therefore the required value of slope is $2$ and value of $y$ intercept is $0$.

Note: In this case we are lucky to have the equation of the line already in slope intercept form, but for the general equation of line, slope can be find by differentiating the equation of line with respect to $x$ and the intercepts can be find by putting the respective values of $x\;{\text{and}}\;y$ zero to get $y\;{\text{and}}\;x$ intercepts respectively.Since in the given equation, value of constant term is equals to zero, it means the line will pass through the origin and will have values $x\;{\text{and}}\;y$ intercepts equals zero.