You can put this solution on YOUR website!
Your first question: What are the x-intercept and y-intercepts of a linear equation?
Answer: In definition terms, I will say to you: The point at which a line crosses the y axis is called the y intercept.
The point at which a line crosses the x axis is called the x intercept.
Your second question: What are their coordinates on a graph?
Answer: The coordinates of the x or y intercept on a graphs depends on the equation of the line, of course, but I can say this:
To find the y-intercept, solve for "y" by making x = 0
---When you make "x" = 0, the coordinates for your y intercept will be: (0,y)
To find the x-intercept, solve for "x" by making y = 0
---When you make "y" = 0, the coordinates for the x intercept will be: (x, 0)
Your third question: How can they be used to graph a line?
Answer: Let's say you know your Y intercept is (0, 4) and your x intercept is (5, 0). You can find those two points on the coordinate plane and then draw a line between the two dots - connect the dots, I mean. That's how you can draw your line. In other words, finding the "x" and "y" intercepts will tell you the point where the line crosses each axis. By knowing those points, you can draw your line.
Your fourth question: Demonstrate by determining the intercepts of
"6x + 9y = 18”
Ok, here is your equation:
6x + 9y = 18 Let's find the y intercept first.
6(0) + 9y = 18 To find the y intercept, solve for y by making x = 0.
0 + 9y = 18 <--Multiply 6 times 0 and you end up with this equation.
9y = 18
Divide both sides by 9 to isolate the y
y = 2
SO now we know that when x = 0, then y = 2.
Our coordinate for the y intercept is: (0, 2)
Now to find the x intercept............
6x + 9y = 18
6x + 9(0) = 18 To find the x intercept, solve for x by making y = 0
6x + 0 = 18 <--Multiply 9 times 0 and you get this equation
6x = 18
Divide both sides by 6 to isolate the x
x = 3
SO now we know that when y = 0, then x = 3
Our coordinate for the x intercept is: (3, 0)
If you put (3,0) and (0, 2) on a coordinate plane and then connect the dots, you will see the line that is formed by the equation of 6x + 9y = 18.
I hope this helps. :-)