Question

How do you find the slope and intercept of $y = 3x + 4$?

Answer 1

We will use the general form of equation of a line in slope-intercept form. We will compare the given equation with the general form and find the slope and the intercept. 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.

Complete step by step solution:
The slope of a line is defined as the ratio of the change in $y$ over the change in $x$ between any two points. The $y$ - intercept of a line is the point on the $y$ - axis where the line cuts the $y$ - axis.
The equation of a line can be represented in slope-intercept form as $y = mx + c$, where $m$ represents the slope of the line and $c$ represents the $y$ - intercept.
We are required to find the slope and intercept of the line $y = 3x + 4$. Let us compare this equation with the general form $y = mx + c$.

We observe that the slope of the given line is $m = 3$ and the $y -$intercept is $c = 4$.

Note:
An alternate way to find the slope of a line is by using the differentiation method.
We know that differentiation means “change in a variable with respect to the change in another variable”, which is exactly what slope also means.
So, if we differentiate the equation of the given line $y = 3x + 4$ with respect to $x$, we will get the slope.
Differentiating both sides with respect to $x$, we have
Slope $= \dfrac{{dy}}{{dx}} = 3$
It must also be noted that if $\theta$ is the angle made by the line with the $x -$ axis, then the tangent of $\theta$ gives the slope of the line i.e., Slope $= \tan \theta$.