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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