Question

How do write \[y-1=\dfrac{4}{5}\left( x+5 \right)\] in slope intercept form?

Answer 1

Hint: This type of problem is based on the concept of equation of lines. First, we need to use distributive property in the given equation, that is, \[a\left( b+c \right)=ab+ac\]. Then, take the ‘y’ term in the left hand side and ‘x’ term in the right hand side of the given equation. We then make the necessary calculations to obtain the required solution of the given equation, that is, to obtain the slope intercept form \[y=mx+c\].

Complete step-by-step answer:
According to the question, we are asked to find the slope intercept form of the given equation \[y-1=\dfrac{4}{5}\left( x+5 \right)\].
We have given the equation is \[y-1=\dfrac{4}{5}\left( x+5 \right)\] -----(1)
From distributive property, we know that \[a\left( b+c \right)=ab+ac\]. Let us use this result in equation (1).
\[\Rightarrow y-1=\dfrac{4}{5}x+\dfrac{4}{5}\times 5\]
On further simplification, we get,
\[\Rightarrow y-1=\dfrac{4}{5}x+4\] -----(2)
Let us add 1 on both sides of the equation (2).
\[\Rightarrow y-1+1=\dfrac{4}{5}x+4+1\]
\[\Rightarrow y=\dfrac{4}{5}x+5\] -----(3)
Compare equation (3) with slope intercept form of a line, that is, \[y=mx+c\].
Therefore, the slope intercept form of the given equation is \[y=\dfrac{4}{5}x+5\].
Where \[m=\dfrac{4}{5}\] and c=5.
Hence, the slope intercept form of the given equation \[y-1=\dfrac{4}{5}\left( x+5 \right)\] is \[y=\dfrac{4}{5}x+5\].

Note: Whenever you get this type of problem, we should try to make the necessary calculations in the given equation to get the final answer in slope intercept form. We should avoid calculation mistakes based on sign conventions. We can also solve this question by multiplying the given equation, that is, \[5\left( y-1 \right)=4\left( x+5 \right)\]. Then use distributive property and make some necessary calculations to obtain the final answer.