Question

How do you find the slope and the intercept for $y = 10 + 3x$?

Answer 1

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 answer:
We are given that an equation of a line is given by $y = 10 + 3x$.
Now consider the given equation, as shown below:
$\Rightarrow y = 10 + 3x$
Here the slope of the equation is obtained when expressed the given equation in slope-intercept form as given below:
Rearrange the equation such that the $y$ term is on the left hand side of the equation, whereas the $x$ term and the constant 10 is on the right hand side of the equation, as given below:
$\Rightarrow y = 3x + 10$
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 given by:
$\Rightarrow m = 3$
Whereas the y-intercept is given by:
$\Rightarrow c = 10$
The intercept is positive. Hence the line is not passing through the origin with a positive slope.

The slope and the intercept of $y = 10 + 3x$ are 3 and 10.

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.