Question

What is the slope and y–intercept of the line $y=3x+2$?

Answer 1

Write the given equation in the slope intercept form by taking the variable y to the L.H.S and all other terms to the R.H.S, make the coefficient of y equal to 1. Now, compare the given linear equation with the slope – intercept form of a line given as $y=mx+c$. Here, ‘m’ is the slope of the line and ‘c’ is its y – intercept. Write the respective values of m and c to get the answer.

Complete step by step solution:
Here we have been provided with the linear equation $y=3x+2$ and we have been asked to find the slope and y – intercept of this line. Let us first we know about the slope – intercept form of a linear equation.
Now, we know that we can write a linear equation of a straight line in many forms like: - standard form, slope – intercept form, polar form, parametric form etc. But here we need to see the slope – intercept form.
In slope – intercept form we write the equation of a line as $y=mx+c$, where ‘m’ represents the slope and ‘c’ represents the intercept on y – axis. In the provided equation $y=3x+2$ we can see that it is already in the slope – intercept form. Here, we have the coefficient of x as m = 3 and the constant term as c = 2, so we can conclude the following results about this line: -
$\therefore$ Slope (m) = 3 and y – intercept (c) = 2.

Note: Note that you can also convert the given equation of line into the standard form given as $ax+by+c'=0$. Here, slope is given as $\dfrac{-b}{a}$ and the y – intercept for this form is given as $\dfrac{-c'}{a}$. In the intercept form we write the equation as $\dfrac{x}{a}+\dfrac{y}{b}=1$ where ‘a’ and ‘b’ are the x – intercept and y – intercept respectively.