Question

How do you find the slope and intercept of $y = \dfrac{3}{5}x - 1?$

Answer 1

Hint : These types of questions involve the operation of addition/ subtraction/ multiplication/ division. We need to know the basic equation for a straight line. We need to compare the given equation in the question with the basic form of the straight-line equation. Also, we need to know which one is the slope and which one is intercepting in the straight-line equation.

Complete step-by-step answer :
The given equation is shown below,
$y = \dfrac{3}{5}x - 1 \to \left( 1 \right)$
The basic equation for a straight line is given below,
$y = mx + c \to \left( 2 \right)$
In the above equation $m$ is the value of slope and $c$ is the value of intercept.
To find the value of slope and intercept from the given question we would compare the equation $\left( 1 \right)$ and $\left( 2 \right)$ . So let’s compare the equation $\left( 1 \right)$ and $\left( 2 \right)$ , we get
$\left( 1 \right) \to y = \dfrac{3}{5}x - 1$
$\left( 2 \right) \to y = mx + c$
Let’s compare the $x$ terms in the equation $\left( 1 \right)$ and $\left( 2 \right)$ , we get
$m = \dfrac{3}{5}$
Let’s compare the constant terms in the equation $\left( 1 \right)$ and $\left( 2 \right)$ , we get
$c = - 1$
So, we know that, $m$ is the slope and $c$ is the intercept. So, the final answer is,
The slope of $y$ is $\dfrac{3}{5}$ and the intercept of $y$ is $- 1$ .
So, the correct answer is “The slope of $y$ is $\dfrac{3}{5}$ and the intercept of $y$ is $- 1$ ”.

Note : The given question involves the operation of addition/ subtraction/ multiplication/ division. Note that the denominator value would not be equal to zero. We would compare the $x$ term in one equation with the $x$ term in another equation to make an easy calculation. In the same way, we would compare the constant terms in two-equation. Remember the basic equation for a straight line. Note that $m$ be the slope of the given equation $y$ and $c$ be the intercept of the given equation $y$ .