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# Find the slope and intercept of the line $y = 6 - x$.

Last updated date: 26th Feb 2024
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Hint: Rewrite the equation in the $y = mx + c$ form and then find the slope represented by $m$ and the $y -$ intercept represented by $c$.

Complete step by step solution:
The slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.
The $y -$ intercept of this line is the value of $y$ at the point where the line crosses the $y$ axis.
The given equation is $y = 6 - x$. Rewrite this in the standard form of a line that is $y = mx + c$, where $m$ is the slope of the line and $c$ is its $y -$ intercept.
Given : $y = 6 - x$
$\Rightarrow y = - x + 6$
Comparing with the $y = mx + c$ form:
$m = - 1$ and $c = 6$

Hence slope of the line is equal to $- 1$ and $y -$ intercept is $6$.

Note:
Students must also know that for any line of the form $Ax + By + C = 0$,
The slope $m$ $=$ $\dfrac{{ - A}}{B}$
$y -$ intercept $=$ $\dfrac{{ - C}}{B}$
Considering the given question observe the equation can be re-written as :
$x + y - 6 = 0$
Comparing it with $Ax + By + C = 0$ form,
$A = 1$, $B = 1$, $C = - 6$
$\therefore$ slope $=$ $\dfrac{{ - A}}{B}$ $=$ $\dfrac{{ - 1}}{1}$ $=$ $1$
$\therefore$ $y -$ intercept $=$ $\dfrac{{ - C}}{B}$ $=$ $\dfrac{{ - \left( { - 6} \right)}}{1}$ $=$ $6$.