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Question 74223: graph
a)by finding the x- and y-intercept: x-3y=-6
b)x-4y=-8
Found 2 solutions by rmromero, bucky:
Answer by rmromero(383)   (Show Source):
You can put this solution on YOUR website!
graph
a) by finding the x- and y-intercept : x-3y=-6
Two points determine a line.WE need two points then.
The x-intercept and the y-intercept
To find x-intercept , y = 0. Substitute it to x-3y=-6
x - 3(0) = -6
x = -6
First point is located (-6,0)
To find y -intercept, x = 0.Substitute it to x-3y=-6
0 - 3y = -6
-3y = -6
y = 2
second point is located (0, 2)
graphing time
b)by using the slope and y-intercept : x-4y=-8
Slope - intercept form is y = mx + b, where m = slope and b = y-intercept
we will rewrite the given equation to slope - intercept form
x + 8 = 4y
x 8
___ + ___ = y
4 4
1
___x + 2 = y
4
m = 1/4 and b = 2
The first point is located using b which is the y - intercept (0,2)
Using the y -intercept, the slope help us locate the next point
The numerator represents the change in y and denominator the change in x
from (0,2) we move 1 unit up (up for positive)
and 4 unit right (right for positive)
Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website! find the x- and y-intercept of:
,
x-3y=-6 and
.
x-4y=-8
.
Think about graphing. If a point of the form (x,y) has a zero value of x, then the y
value has to be on the y-axis. Similarly, if a point of the form (x,y) has a zero value for
y then the value for x has to be on the x-axis.
.
To demonstrate these two ideas, try plotting the point (0,6) you will see that it lies on
the y-axis 6 units up from the origin. This is because the x value is zero ... and that
requires the corresponding value of y to be on the y-axis.
.
Next try plotting the point (3,0). You will go out 3 units on the x-axis but that is
where you will stay because the corresponding value of y is 0.
.
In summary we can say that when x = 0, the corresponding value for y is on the y-axis and
when y = 0, the corresponding value for x is on the x-axis.
.
Now go to the first equation which is:
.
x - 3y = -6
.
If we set x equal to zero we will find the corresponding value of y that is on the y-axis.
When x is zero in this equation, the equation is reduced to:
.
-3y = -6
.
Dividing both sides by -3 results in y = 2. So our point is x = 0 and y = 2 or just (0,2)
and this is on the y-axis which means that it is the y-intercept.
.
If we then return to the equation, but this time we set y = 0 the equation reduces to
.
x = -6
.
because y is equal to 0, this point is on the x-axis as we discussed above. This point
is (-6,0) which means that it is the x-intercept. Now you can plot the two points
(0,2) and (-6,0) and these two points can be connected by a straight line running
through them, and this line is the graph of the equation x - 3y = -6.
.
The same thing can be done with the second equation: x - 4y = -8
.
First, set x = 0 and solve the equation for y. With x = 0 the equation becomes just:
.
-4y = -8
.
Divide both sides by -4 and you get y = 2. So the point (0,2) is on the graph. It is
also on the y-axis and is the y-intercept.
.
Then set y = 0 in the equation. When you do the equation reduces to just:
.
x = -8
.
So the point (-8,0), which is on the x-axis is also on the graph and is the x intercept.
Plot the two points (0,2) and (-8,0) and extend a line through them. This is the graph
of this equation.
.
Hope this helps you to understand how to get the x and y intercepts from a linear equation.
Just set x equal to zero to get the y intercept and next set y equal to zero to get the
x intercept.
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