1. Identify and Graph Linear Equations Name and Graph X and Y Intercepts
Linear Functions
Identify and Graph Linear Equations
Name and Graph X and Y Intercepts

2. Vocabulary for this lesson
Linear Equation – the equation of a line whose graph is a straight line.
Standard Form – Linear equations written in the form Ax + By + C= 0
X-Intercept – the point where a graphed line crosses the x-axis.
Y-Intercept – the point where a graphed line crosses the y-axis.

3. Determine whether each equation is linear…
Determine whether each equation is linear….if so, write it in Standard Form
Can it be written in standard form? Ax + By = C
1) y = 5 – 2x
Yes
+2x x
2x + y = 5
2) y = -3 – x
Yes
+ x x
x + y = -3
3) 2xy – 5y = 6 No
Why?....The first term has TWO variables.

4. Another way to look at this.....
(3)
(3)
4) 1/3 y = -1
Yes
y = -3
Can it be written in standard form? Ax + By = C
5) 5x + 3y = z + 2 No
Why?....It has an extra variable “z”.
6) y = x2 – 8 No
Why?....Because the “x” is squared.
Another way to look at this.....
To be considered LINEAR, an equation must have a degree of ONE.

5. x and y - Intercepts To find the x-intercept, let y = 0
To find the y-intercept, let x = 0
The x-int. is 7, so the graph intersects the x-axis at (7, 0)
The y-int. is -2, so the graph intersects the y-axis at (0, -2)

6. You can also graph using the intercepts.
x-intercept (7, 0)
y-intercept (0, -2)
Now, draw a line through the points.

7. Find the x & y intercepts, then graph the equation.
(-5, 0)
(0, -5)

8. Find the x & y intercepts, then graph the equation.
(3, 0)
0 + 2y = 9
2y = 9
y = 4.5
(0, 4.5)

9. Determine the x & y intercepts of each linear function.
10)
11) x y -3 -1 -2 1 2 3
y-int. = 3
or (0, 3)
x-int. = -4
or (-4, 0)
x-int = -2
Or (-2, 0)
y-int = 2
Or (0, 2)

10. Real World Examples
x-int. of 20 means that after 20 minutes, the temperature was 0°F.
y-int. of -4 means that at 0 time (the beginning) the temperature was °F
x-int. = 20 or (20, 0)
12) Determine the x & y intercepts
and describe what the intercepts mean.
y-int. = -4 or (0, -4)

11. Real World Examples
Determine the x & y intercepts and describe what they mean.
x-int. = -3 or (-3, 0)
y-int. = or (0, 2.25)
The x-int. doesn’t make sense here because it is negative.
The y-int. represents the base fare, or cost at zero miles.

12. Determine the Intercepts and explain each.
14) Draining a pool
15) Position of a scuba diver.
Time (h)
Volume (g)
10,080 2
8640 4
7200 6
5760 8
4320 10
2880 14
The x-int. shows that after 12 sec., the diver was at the surface (0 m). The y-int. shows that when he started (0 s) he was at -24m or 24m below sea level.
Time (s)
Depth (m)
-24 3
-18 6
-12 9 -6 12
The x-int. shows that after 14 hours, the pool had 0 gallons, or it was completely drained. The y-int. shows that at 0 hours, when they began, it had 10,080 gallons in it.

13. Exercise

14. Challenge