Question

How do you find the slope and intercept of $y = 2x - 3$ ?

Answer 1

Hint : In order to determine the slope and intercept to the above equation first rewrite the equation as $y = 2x + ( - 3)$ and compare with the slope-intercept form $y = mx + c$ , 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. $y = 2x - 3$
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
$y = 2x + ( - 3)$ comparing with slope-intercept form $y = mx + c$
So
$m = 2 \\\ c = - 3 \;$
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.
y-intercept as $(0, - 3)$ with slope $m = 2$
So, the correct answer is “y-intercept as $(0, - 3)$ with slope $m = 2$ ”.

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 line , the one which is horizontal is given name x-axis and the one which is vertical is known as y-axis. With the help of these axis we can plot any point on this cartesian plane with the help of an ordered pair of numbers.
2.Slope-Intercept Form= $y = mx + c$