Find the
x
- and
y
-intercepts (if they exist), and graph the line.
5x-4y=5
X intercept:
Y intercept:
To find the x-intercept, we set y equal to 0 and solve for x:
5x - 4(0) = 5
5x = 5
x = 1
So the x-intercept is at (1, 0).
To find the y-intercept, we set x equal to 0 and solve for y:
5(0) - 4y = 5
-4y = 5
y = -5/4
So the y-intercept is at (0, -5/4).
Now let's graph the line. To do this, we can plot the x-intercept (1, 0) and the y-intercept (0, -5/4) and then draw a straight line connecting them.
Find the
x
- and
y
-intercepts (if they exist), and graph the line.
2x-3y=−3
To find the x-intercept, we set y equal to 0 and solve for x:
2x - 3(0) = -3
2x = -3
x = -3/2
So the x-intercept is at (-3/2, 0).
To find the y-intercept, we set x equal to 0 and solve for y:
2(0) - 3y = -3
-3y = -3
y = 1
So the y-intercept is at (0, 1).
Now let's graph the line. To do this, we can plot the x-intercept (-3/2, 0) and the y-intercept (0, 1) and then draw a straight line connecting them.
Find the
x
- and
y
- intercepts (if they exist), and graph the line.
2x-3y=0
To find the x-intercept, we set y equal to 0 and solve for x:
2x - 3(0) = 0
2x = 0
x = 0
So the x-intercept is at (0, 0).
To find the y-intercept, we set x equal to 0 and solve for y:
2(0) - 3y = 0
-3y = 0
y = 0
So the y-intercept is at (0, 0).
Now let's graph the line. Since both intercepts are at (0, 0), this means the line passes through the origin. Thus, the graph is a straight line passing through the point (0, 0).
Find the
x
- and
y
- intercepts (if they exist), and graph the line.
x=-4y
To find the x-intercept, we set y equal to 0 and solve for x:
x = -4(0)
x = 0
So the x-intercept is at (0, 0).
To find the y-intercept, we set x equal to 0 and solve for y:
0 = -4y
y = 0
So the y-intercept is at (0, 0).
Now let's graph the line. Since both intercepts are at (0, 0), this means the line passes through the origin. Thus, the graph is a straight line passing through the point (0, 0).
For X=3,
(a) Identify the equation as representing a horizontal or vertical line.
(b) Graph the line.
(c) Identify the x- and y-intercepts if they exist.
(a) The equation x = 3 represents a vertical line.
(b) To graph the line, we draw a vertical line passing through the point (3,0).
(c) Since the line is vertical, it does not intersect the y-axis (y-intercept). However, the x-intercept can be found by setting y equal to 0 and solving for x:
x = 3
So the x-intercept is at (3,0).