Question

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

Answer 1

In this question, we have to find out the slope and intercept of the given equation.
To find the slope and intercept we will compare the equation with slope-intercept form of a linear equation$y = mx + b$,
Where m = slope of the linear equation.
b = y-intercept value of the linear equation. On doing some simplification we get the required answer.

Complete step by step answer:
We have to find out the slope and intercept of $y = 4x$.
We know that the slope-intercept form of a linear equation is $y = mx + b$……i),
Where m = slope of the linear equation.
b = y-intercept value of the linear equation.
Now we can write the given equation as $y = 4x + 0$……...ii)
Comparing equation i) and ii) we get,
The slope is: $m = 4$.
The y-intercept is: $b = 0$

Hence, the slope of $y = 4x$ is $4$ and the intercept is $0$.

Note: Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line.
Another method for finding slope:
To find the slope m of a curve at a particular point, we differentiate the equation of the curve. If the given curve is $y = f\left( x \right)$ we evaluate $\dfrac{{dy}}{{dx}}$ or $f'\left( x \right)$ and substitute the value of x to find the slope.
Here the given equation is$y = 4x$.
thus we get, $\dfrac{{dy}}{{dx}} = 4$.
Hence the slope of the equation is $4$.