Question

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

Answer 1

Hint: 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 \[ = \tan \theta \].