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# How do you find the slope and intercept of $x + y = 9$?

Last updated date: 23rd Feb 2024
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Hint:In order to determine the slope and intercept to the above equation first rewrite the equation in such a way that the left side of the equation contain only variable $y$ , $y = - x + 9$ and compare with the slope-intercept form $y = mx + c$, m is the slope and c is the y-intercept.

Complete step by step solution:
We are given a linear equation in two variables $x\, and \,y$ i.e. $x + y = 9$
Rewriting the above equation such that the left-hand side of the equation contains only variable $y$.
$x + y = 9$
Transposing the term having variable $x$ to the RHS, we get
$y = - x + 9$
To determine the slope and intercept of the above equation comparing it with the slope-intercept form $y = mx + c$
Where, m is the slope and c is the y-intercept.
$y = - x + 9$ comparing with slope-intercept form $y = mx + c$
So $m = - 1 \\ c = 9 \\$
Let's graph the equation, we are jumping on the cartesian plane.
There is one most important property of a plane that graphs the equation of form $ax + by + c = 0$ is always a straight line.
Graph of equation having y-intercept as $(0,9)$with slope $m = - 1$

Hence we’ve successfully plotted graph of $x + y = 9$
Therefore, the slope and intercept to the expression$x + y = 9$ is equal to $- 1\,\,and\,\,9$ respectively.

2.Slope-Intercept Form= $y = mx + c$
2.Slope of line perpendicular to the line having slope $m$is equal to $- \dfrac{1}{m}$.