Question

Find the slope and intercept of $y=5x-7$?

Answer 1

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 $\text{b}$.