Question
Lesson 10 graphing linear equation portfolio
Answers
GPT 3.5
In this portfolio, we will be graphing linear equations using different methods: plotting points, using the slope-intercept form, and finding the x-intercept and y-intercept.
1. Graphing linear equation: y = 2x + 1
To graph this equation, we can use the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 1.
To graph the line, we can plot the y-intercept at (0, 1) and then use the slope to find another point. The slope of 2 means that for every 1 unit we move to the right, we move 2 units up. So we can plot another point at (1, 3) and connect the two points to graph the line.
2. Graphing linear equation: 3x - 2y = 6
To graph this equation, we can rewrite it in slope-intercept form, y = mx + b. First, we can isolate the y variable by subtracting 3x from both sides and then dividing by -2:
-2y = -3x + 6
y = 3/2x - 3
Now we can graph the line using this form. The y-intercept is -3, so we can plot the point (0, -3) on the y-axis. The slope of 3/2 means that for every 2 units we move to the right, we move 3 units up. So we can plot another point at (2, 0) and connect the two points to graph the line.
3. Graphing linear equation: x - 4y = 8
To graph this equation, we can rewrite it in slope-intercept form, y = mx + b. First, we can isolate the y variable by subtracting x from both sides and then dividing by -4:
-4y = -x + 8
y = 1/4x - 2
Now we can graph the line using this form. The y-intercept is -2, so we can plot the point (0, -2) on the y-axis. The slope of 1/4 means that for every 4 units we move to the right, we move 1 unit up. So we can plot another point at (4, 0) and connect the two points to graph the line.
In conclusion, graphing linear equations can be done using different methods, such as plotting points, using the slope-intercept form, and finding the x-intercept and y-intercept. These methods can help us visualize and understand the relationship between the variables in a linear equation.
1. Graphing linear equation: y = 2x + 1
To graph this equation, we can use the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope is 2 and the y-intercept is 1.
To graph the line, we can plot the y-intercept at (0, 1) and then use the slope to find another point. The slope of 2 means that for every 1 unit we move to the right, we move 2 units up. So we can plot another point at (1, 3) and connect the two points to graph the line.
2. Graphing linear equation: 3x - 2y = 6
To graph this equation, we can rewrite it in slope-intercept form, y = mx + b. First, we can isolate the y variable by subtracting 3x from both sides and then dividing by -2:
-2y = -3x + 6
y = 3/2x - 3
Now we can graph the line using this form. The y-intercept is -3, so we can plot the point (0, -3) on the y-axis. The slope of 3/2 means that for every 2 units we move to the right, we move 3 units up. So we can plot another point at (2, 0) and connect the two points to graph the line.
3. Graphing linear equation: x - 4y = 8
To graph this equation, we can rewrite it in slope-intercept form, y = mx + b. First, we can isolate the y variable by subtracting x from both sides and then dividing by -4:
-4y = -x + 8
y = 1/4x - 2
Now we can graph the line using this form. The y-intercept is -2, so we can plot the point (0, -2) on the y-axis. The slope of 1/4 means that for every 4 units we move to the right, we move 1 unit up. So we can plot another point at (4, 0) and connect the two points to graph the line.
In conclusion, graphing linear equations can be done using different methods, such as plotting points, using the slope-intercept form, and finding the x-intercept and y-intercept. These methods can help us visualize and understand the relationship between the variables in a linear equation.