The graph of the lines is as shown in following figure.
1) for line y = 2
slope = 0
x-intercept = 0
y-intercept = 2
2) for line [tex]y=-\frac{1}{2}x[/tex]
slope = [tex]-\frac{1}{2}[/tex]
x-intercept = 0
y-intercept = 0
3) for line x - y = 4
slope = 1
x-intercept = 4
y-intercept = -4
4) for line x = -1
slope = undefined
x-intercept = -1
y-intercept = 0
What is the graph?
"It is the set of points which makes the equation true."
What is slope-intercept form of a line?
The slope-intercept form of a line is, y = mx + c
where m is the slope and c is the y-intercept
What is x-intercept?
"The point at which the graph of a function intersects the x-axis."
What is y-intercept?
"The point at which the graph of the function intersects the y-axis."
For given question,
Consider a line
1) y = 2
The graph of the line y = 2 is the straight line passing through point (0, 2) and parallel to x-axis.
If we compare above equation of line with slope-intercept form,
We have m = 0 and c = 2
This means for the line y = 2,
slope = 0
x-intercept = 0
y-intercept = 2
2) [tex]y=-\frac{1}{2}x[/tex]
The graph of the line [tex]y=-\frac{1}{2}x[/tex] is the straight line passing through origin with slope m = -1/2.
Since the slope of the line is negative, it passes through the second and fourth quadrant.
If we compare above equation of line with slope-intercept form,
We have m = -1/2 and c = 0
This means for the line [tex]y=-\frac{1}{2}x[/tex],
slope = [tex]-\frac{1}{2}[/tex]
x-intercept = 0
y-intercept = 0
3) x - y = 4
We write it above equation in slope-intercept form of line.
⇒ x - y = 4
⇒ -y = 4 - x
⇒ (-1) × (-y) = (-1) × (4 - x)
⇒ y = x - 4 .........................(a)
For x = 0,
y = -4
and for y = 0,
x = 4
The graph of the line x - y = 4 is the straight line passing through points (0, -4) and (4, 0)
If we compare equation (a) with slope-intercept form,
We have m = 1 and c = -4
This means for the line x - y = 4,
slope = 1
x-intercept = 4
y-intercept = -4
4) x = -1
The graph of the line x = -1 is the straight line passing through point (-1, 0) and parallel to y-axis.
We know, the slope of a line parallel to the y-axis is undefined.
This means for the line x = -1,
slope = undefined
x-intercept = -1
y-intercept = 0
Therefore, the graph of the lines is as shown in following figure.
1) for line y = 2
slope = 0
x-intercept = 0
y-intercept = 2
2) for line [tex]y=-\frac{1}{2}x[/tex]
slope = [tex]-\frac{1}{2}[/tex]
x-intercept = 0
y-intercept = 0
3) for line x - y = 4
slope = 1
x-intercept = 4
y-intercept = -4
4) for line x = -1
slope = undefined
x-intercept = -1
y-intercept = 0
Learn more about the slope and intercept of the line here:
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