Question

Find the slope and intercept of \[y=5x-7\]?

Answer 1

Hint: In order to find slope and intercept of a given line we will consider a slope – intercept form of line and compare it with the given equation of line, on comparing these two equations of lines we will get our required.

Complete Step by Step Solution:
The line equation is
\[y=mx+b\] ....(i)
 Now, we have given the line equation in the question is as follows:
\[y=5x-7\] .…(ii)
Now, we will compare the equation (i) and equation (ii) and we will get,
\[m=5\] and \[b=-7\]
Which implies that the slope of the given line equation is m = -5 and the y-intercept of the given line equation is \[b=7\].

Note: Slope of line: The slope of line characterizes the direction of a line.
In order to find the slope of a line we have to divide the difference of \[\text{y}\] coordinates of two points on a line by the difference of the \[\text{x}\] coordinates of those same two points.
Also, there are some important forms for the equation of line which we have to always remember.
• Slope intercept form of line equation is given as: \[y=mx+b\];
This formula is used when we have given the slope and the \[\text{y}\] intercept of the line.
• Standard form of the line equation is given as: \[Ax+Bx+c\].
• Point slope form of the line equation is given as: \[\left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right)\].
This formula is used when we have given slope of line and point on the line.
• Two intercept forms of line equation are given as: \[\dfrac{x}{a}+\dfrac{y}{b}=1\].
This formula is used when we have both intercepts given.
• Vertical line equation is given as: \[x=a\].
This formula is used when all points have \[\text{x}\]-coordinates as \[\text{a}\].
• Horizontal line equation is given as: \[y=b\]
This formula is used when all points have \[\text{y}\]-coordinates as \[\text{b}\].