Graph the linear function y=-2x+3
How do I work this out?
do you have some graph paper?
pick any value for x, and calculate y. The easiest value to use is x=0. Then y=3. So, the point (0,3) is on the graph.
For y, if you pick and even value, you will have a fraction for x, so pick any odd value, say, y=1. Then x=1, and (1,1) is on the graph.
Plot those two points on the graph paper, and connect them with a line. All done, except for labeling stuff.
You could have picked lots of other values for x and y, but they'd all have to be on the same line -- any two points on the line will do to get started.
To graph the linear function y = -2x + 3, you can use the slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
1. Identify the slope and y-intercept:
- The slope (m) of the equation is -2.
- The y-intercept (b) is 3.
2. Plot the y-intercept:
- Start by plotting the point (0, b), which in this case is (0, 3). This is where the line crosses the y-axis.
3. Determine additional points using the slope:
- Since the slope is -2, you can use it to find other points on the line.
- For simplicity, we'll solve for x = 1 and x = -1:
- For x = 1:
- Substitute x = 1 into the equation: y = -2(1) + 3 = -2 + 3 = 1.
- This gives you the point (1, 1).
- For x = -1:
- Substitute x = -1 into the equation: y = -2(-1) + 3 = 2 + 3 = 5.
- This gives you the point (-1, 5).
4. Plot the additional points:
- Plot the points (1, 1) and (-1, 5) on the graph.
5. Connect the points:
- Use a straight edge or ruler to draw a line passing through the points (0, 3), (1, 1), and (-1, 5).
- The line should extend infinitely in both directions.
You have now graphed the linear function y = -2x + 3.