Question
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Answer
Plot the points (0, -1) and (1, 1) and draw a line through them. The slope is 2.
Solution
To graph the equation
, we can follow these steps:
-
Identify the slope and y-intercept: The equation is in the slope-intercept form
, where is the slope and is the y-intercept. Here, the slope and the y-intercept . -
Plot the y-intercept: Start by plotting the point where the line crosses the y-axis. This occurs at
. -
Use the slope to find another point: The slope of 2 means that for every 1 unit you move to the right (positive direction on the x-axis), you move up 2 units (positive direction on the y-axis). From the point
: - Move 1 unit to the right to
. - Move up 2 units to
. - Plot the point
.
- Move 1 unit to the right to
-
Draw the line: Connect the points
and with a straight line. Extend the line in both directions. -
Label the axes: Make sure to label the x-axis and y-axis for clarity.
The graph of the equation
is a straight line that passes through the points
and
, with a slope of 2.
If you need a visual representation, you can use graphing software or graphing calculators to plot it accurately.
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Extra Insights
To graph the equation
, start by plotting the y-intercept, which is -1 (the point (0, -1) on the graph). Then use the slope, which is 2, indicating that for every 1 unit you move to the right along the x-axis, you rise 2 units on the y-axis. From the y-intercept, move right 1 unit to
and up 2 units to
(the point (1, 1)). Draw a straight line through these points, and you’ll have your graph!
Next, you can also check your work by substituting a few x values. For instance, if x=2, then
, giving you the point (2, 3). Adding this to your graph will confirm that the line remains consistent, ensuring your graph is accurate and sharp!