Question

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

Answer 1

Hint: 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 \[4\].