Question

How do you graph $y = 5x - \dfrac{5}{2}$ using slope and intercept?

Answer 1

Hint: First of all this is a very simple and a very easy problem. The general equation of a slope-intercept form of a straight line is $y = mx + c$, where $m$ is the gradient and $y = c$ is the value where the line cuts the y-axis. The number $c$ is called the intercept on the y-axis. Based on this provided information we try to find the equation of the straight line.

Complete step-by-step solution:
We are given that an equation of a line is given by $y = 5x - \dfrac{5}{2}$.
Now consider the given equation, as shown below:
$ \Rightarrow y = 5x - \dfrac{5}{2}$
Here the slope of the equation is obtained when expressed the given equation in slope-intercept form as given below:
Here the given equation of the line is already expressed in the form of slope-intercept form.
Here the above equation is expressed in the form of the slope intercept form which is $y = mx + c$.
The slope of the equation is as given below:
$ \Rightarrow m = 5$
Whereas the y-intercept is given by:
$ \Rightarrow c = - \dfrac{5}{2}$
The intercept is negative. Hence the line is not passing through the origin with a positive slope.

The slope and the intercept of $y = 5x - \dfrac{5}{2}$ is 5 and $ - \dfrac{5}{2}$ respectively.

Note: Please note that while solving such kind of problems, we should understand that if the y-intercept value is zero, then the straight line is passing through the origin, which is in the equation of $y = mx + c$, if $c = 0$, then the equation becomes $y = mx$, and this line passes through the origin, whether the slope is positive or negative.