Question

How do you find the slope and intercept of \[y=\dfrac{2}{3}\left( 2x-4 \right)\]?

Answer 1

Hint: A straight line in the form \[y=mx+c\]. \[y\] and \[x\] are variables, m is called slope, and c is called intercept on the y-axis. The slope tells us how steeper the line is, if the slope is positive then the line slope moves up to the right and if the slope is negative then the slope of the line moves down. c is also called \[y-\]intercept. To solve the above equation we use the distributive property to expand the equation and then compare with the line \[y=mx+c\] and then find the slope and intercept of the straight line. Distributive property means \[a\left( b+c \right)=ab+ac\].

Complete step by step answer:
As per the given question, we need to find the slope and intercept of the given straight line \[y=\dfrac{2}{3}\left( 2x-4 \right)\].
The above equation doesn’t look like it in the form \[y=mx+c\]. So we expanded the bracket. To expand the bracket we use the distributive property \[a\left( b+c \right)=ab+ac\] to expand the equation.
 Then the equation becomes
\[\Rightarrow \]\[y=\dfrac{2}{3}\times 2x-\dfrac{2}{3}\times 4\]
We know that, \[\dfrac{2}{3}\times 2x\] is equal to \[\dfrac{4}{3}x\]; \[\dfrac{2}{3}\times 4\] is equal to \[\dfrac{8}{3}\]. By substituting all these terms into the previous equation, we get
 \[\Rightarrow y=\dfrac{4}{3}x-\dfrac{8}{3}\]
We can rewrite the equation as
\[\Rightarrow y=\dfrac{4}{3}x+\left( -\dfrac{8}{3} \right)\]
Now we compare the above equation with \[y=mx+c\]. Then the value of m will be \[\dfrac{4}{3}\] and the value of c will be \[\dfrac{-8}{3}\].
Therefore, the slope of \[y=\dfrac{2}{3}\left( 2x-4 \right)\] is \[\dfrac{4}{3}\] and intercept of \[y=\dfrac{2}{3}\left( 2x-4 \right)\] is \[\dfrac{-8}{3}\].

Note:
In order to solve these types of problems, we need to have knowledge of straight lines and its properties. We also need to have knowledge of arithmetic functions. We should avoid calculation mistakes to get the correct solution.