The first equation we are asked to graph is the simple equation:
x = -1
So, we create a table for it that has in the first column the x values, and in the second column the associated y values.
SInce the equation says x = -1 no matter what the value of y is, we can write any y values in the column for y
We end up with pairs of points of the form:
(-1, 0)
(-1, 2)
(-1, 3)
(-1, 5)
(-1, -4)
and so forth, with all os them having a -1 in the first coordinate (the x-coordinate)
Notice that such points give us a vertical line when we join them, it is a vertical line going through the X = -1 point on the x-axis.
where the line x = -1 is plotted in red.
Now, for the second line that reads:
2 x - 5 y = 5
we solve for y in order to make our calculations easier:
add 5 y to both sides:
2 x = 5 + 5y
subtract 5 from both sides:
2 x - 5 = 5 y
now diide both sides by 5:
y = (2 x - 5) / 5
So, let's find at least three points that define our line
Notice that when x = 5 , we get:
y = (10 - 5) / 5 = 5 / 5 = 1
So we draw the point (5, 1) on the x-y plane
When x = 0 we get:
y = (2 (0) - 5) / 5 = - 5/5 = -1
So we draw the point (0, -1) on the plane
And finally, we use the point x = -5 and get:
y = (2 (-5) - 5) / 5 = -15/ 5 = -3
So we draw the point (-5, -3) on the plae.
Then we draw a line connecting the three points we found, as shown below: