Graph the linear function y=-2x+1.
To graph the linear function y = -2x + 1, we can use the slope-intercept form of a linear equation, which is 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, so we can plot the y-intercept as (0,1) and use the slope to find one or two more points on the line.
Going down in the y-direction by 2 units for each 1 unit we go to the right will give us the next point. So, from the y-intercept at (0,1), we can move down 2 units to (1,-1), and then down another 2 units to (2,-3).
We can continue this pattern indefinitely to draw the line as shown below:
<img src="https://www.onlinemathlearning.com/image-files/graph-linear-equation-example-1.gif">
To graph the linear function y = -2x + 1, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope (m) is -2, and the y-intercept (b) is 1.
To graph the line, we'll start by plotting the y-intercept, which is the point (0, 1). This is where the line crosses the y-axis.
Next, we can use the slope to find additional points on the line. The slope of -2 means that for every unit increase in the x-coordinate, the y-coordinate decreases by 2.
So, starting from the y-intercept (0, 1), we can move 1 unit to the right and 2 units down to get the next point on the line. This gives us the point (1, -1).
We can continue this process to plot more points. For example, if we move 1 unit to the left from the y-intercept, we get the point (-1, 3). Similarly, we can move 2 units to the right and 4 units down from the y-intercept to get the point (2, -3).
Once we have plotted a few points, we can connect them with a straight line to complete the graph.
Here is the graph of the linear function y = -2x + 1: