Algebra I
Linear Equations
Day 6
Name: _____________________
Last class you graphed linear equations that were solved for y, y = mx + b where b is the starting point
of the graph on the y axis and m is the growth rate or slope of the equation. Not every equation comes
in that prepackaged form for graphing. Today we are going to look at equations that are arranged
differently.
Standard Form: Standard form equations are when the x and y variables are on the same side of the
equation. They look like the following:
Example: Find the growth rate and start value for the equation then graph.
- 6x + 3y = 9.
The process of changing a linear equation from standard form to slope intercept form is always the
same:
 Add the opposite of the x-term to each side.
 Divide by the coefficient of the y-term.
Solve each of the equations for y then find the start value and growth rate to graph.
a. 5x + 5y = 25
b. 3x – 6y = 18
c. -5x + 3y = 9
d. 7x – 8y = -32
Using the Intercepts:
There is a second way to draw the graph of a line in standard form that is pretty simple. This
method is by finding the intercepts of the graph. The x-intercepts are where the graph crosses the xaxis, and the y-intercepts are where the graph crosses the y-axis.
To clarify the algebraic part, think again about the axes. When you were first introduced to the
Cartesian plane, you were shown the regular number line from elementary school (the x-axis), and then
shown how you could draw a perpendicular number line (the y-axis) through the zero point on the first
number line. Take a closer look, and you'll see that the y-axis is also the line "x = 0". In the same way,
the x-axis is also the line "y = 0".
Then, algebraically,
 an x-intercept is a point on the graph where y is zero, and
 a y-intercept is a point on the graph where x is zero.
Example: Find the x and y intercepts of the equation then graph the line using the intercepts
- 6x + 3y = 18.
Find the x and y intercepts then graph each of the following equations.
a. 5x + 5y = 25
b. 3x – 6y = 12
c. -5x + 3y = 9
d. 7x – 8y = 54
Solve each of the equations for y then identify the y-intercept and slope. Then graph each
equation on the x-y coordinate grids provided (you may detach x-y grid page from this packet.)
1. 2x + 3y = 15
Y-Int:
Slope:
2. -4x + 5y = 18
Y-Int:
Slope:
3. x + y = 12
Y-Int:
Slope:
4. -3x – y = 12
Y-Int:
Slope:
5. 2x + 5y = 15
Y-Int:
Slope:
6. -6x + 12y = 18 Y-Int
Slope:
Slope:
8. x – y = 8
Slope:
7. 7x – 3y = 12
Y-Int:
Y-Int:
Find the x and y intercepts for the following equations, and use these to graph each equation on
the attached x-y coordinate grids.
9. x + 6y = 6
10. 3x – 6y = -18
11. x + y = 5
12. -3x – y = 12
13. - x - y = 7
14. -8x – 5y = 40
15. 3x + 2y = 12
16. x - y = -2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
16.
14.
15.