Question

How do you graph $2x - 1 = y$ ?

Answer 1

Hint : In order to graph the above equation, consider the fact the graph to any linear function of the form $ax + by + c = 0$ is always a straight line ..As to plot a straight line we require two points. One point is the x-intercept obtained by putting $y = 0$ and another is the y-intercept obtained by putting $x = 0$ in the equation. By plotting, these two points and connect them to obtain the straight line of the equation.

Complete step-by-step answer :
We are given a linear equation in two variables $x\,and\,y$ i.e. $2x - 1 = y$
As we know the graph to a linear function of the form $ax + by + c = 0$ is always a straight line.
So, in order to draw a line, we must have at least two points on the graph which we can connect to form a line.
We’ll be taking one point as y-intercept and another as x-intercept.
To calculate y-intercept of the graph, put $x = 0$ in the equation
$2\left( 0 \right) - 1 = y \\\ y = - 1 \;$
We get y-intercept at point $\left( {0, - 1} \right)$
Now To calculate x-intercept of the graph, put $y = 0$ in the equation
$2x - 1 = y \\\ 2x - 1 = 0 \\\ 2x = 1 \\\ x = \dfrac{1}{2} \\\ x = 0.5 \;$
We get x-intercept at point $\left( {0.5,0} \right)$

X	0	0.5
y	-1	0

Now the graph the equation, we are jumping on the cartesian plan and plot $\left( {0, - 1} \right)$ , $\left( {0.5,0} \right)$ .Joining these two points we get a straight line representing our equation $2x - 1 = y$
Graph of equation having y-intercept as $\left( {0, - 1} \right)$ and x-intercept as $\left( {0.5,0} \right)$ .

Note : 1.Draw the cartesian plane only with the help of straight ruler and pencil to get the perfect and accurate results.
2.Mark the points carefully.
3. x-intercept is the point at which the line intersects the x-axis of the plane and similarly y-intercept is the point at which line intersects the y-axis of the plane.
4.Slope-Intercept Form= $y = mx + c$