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 \[y\] .