Question

How do you find the slope and intercept of $y = 2x + 9?$

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, $y = mx + c$. And to find its x-intercept put the value of $y = 0$ in the given equation then solve for $x$.

Complete step by step answer:
In order to find the slope and intercept of the given equation, let us first understand their meaning. Slope of a line is the change of y-value over the change of the x-value; or rather say it is the gradient of a line. It is also called “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.
So comparing the equation $y = 2x + 9$ to slope intercept form, we will get
$y = 2x + 9\;{\text{and}}\;y = mx + c \\
\Rightarrow m = 2\;{\text{and}}\;c = 9 \\ $
Here we get the values of slope and the y-intercept of the line. Now to find the value of x-intercept, substituting the value of $y = 0$ in the equation $y = 2x + 9$.
$\Rightarrow 0 = 2x + 9 \\
\Rightarrow 2x = - 9 \\
\Rightarrow x = \dfrac{{ - 9}}{2} = - 4.5 \\ $
Therefore the required value of slope is $2$ and values of $x\;{\text{and}}\;y$ intercepts are $ - 4.5\;{\text{and}}\;9$ respectively.

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.