Question

What is the slope and $y$ intercept of the equation $2x + 4y = 12$ ?

Answer 1

Hint : In order to determine the slope and intercept to the above equation first divide both the sides by 2, then rewrite the equation in terms of $y$ and compare with the slope-intercept form $y = mx + c$ , where m is the slope and c is the $y$ intercept.

Complete step-by-step answer :
We are given a linear equation in two variables $x\,and\,y$ i.e $2x + 4y = 12$
Dividing both the sides by 2 and we get:
$\dfrac{{2x + 4y}}{2} = \dfrac{{12}}{2} \\\ x + 2y = 6 \;$
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.
Rewriting our equation $y = \dfrac{{6 - x}}{2} = \dfrac{{ - 1}}{2}x + 3$ , comparing with slope-intercept form $y = mx + c$
So,
$m = \dfrac{{ - 1}}{2} \\\ c = 3 \;$
Now 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 $(0,3)$ with slope $m = \dfrac{{ - 1}}{2}$

Hence, we’ve successfully plotted our graph of $2x + 4y = 12$
Therefore, the slope and y- intercept to expression $2x + 4y = 12$ is equal to $\dfrac{{ - 1}}{2}\,and\,3$ respectively.

Note : 1. Cartesian Plane: A Cartesian Plane is given its name by the French mathematician Rene Descartes, who first used this plane in the field of mathematics. It is defined as the two mutually perpendicular number lines, the one which is horizontal is given the name x-axis and the one which is vertical is known as y-axis. With the help of these axes, we can plot any point on this cartesian plane with the help of an ordered pair of numbers.
2.Slope-Intercept Form= $y = mx + c$