Graphing linear equations portfolio Math 6b

Answer 1

In this portfolio, I will be graphing two linear equations and analyzing their properties.

Equation 1: y = 2x + 3

To graph this equation, we will first make a table of values:

x | y
0 | 3
1 | 5
2 | 7

Plotting these points on a coordinate plane, we get the following graph:

(graph)

Equation 2: y = -3x + 2

Again, we will make a table of values:

x | y
0 | 2
1 | -1
2 | -4

Plotting these points on a coordinate plane, we get the following graph:

(graph)

Analysis:

1. Slope: The slope of Equation 1 is 2, while the slope of Equation 2 is -3. The slope represents the rate of change of the equation.

2. Y-intercept: The y-intercept of Equation 1 is 3, while the y-intercept of Equation 2 is 2. The y-intercept represents the value of y when x is 0.

3. X-intercept: The x-intercept of Equation 1 is -1.5, while the x-intercept of Equation 2 is 0.67. The x-intercept represents the value of x when y is 0.

4. Parallel or perpendicular lines: These two equations are parallel lines because they have different slopes.

5. Relationship between the two equations: Equation 1 has a positive slope, while Equation 2 has a negative slope. This means that as x increases, y increases for Equation 1, but decreases for Equation 2.

Overall, graphing linear equations allows us to visualize the relationship between variables and analyze their properties.