The graph in the image shows a line with a slope of -2 and a y-intercept of 4. This means that the equation of the line is y = -2x + 4
To see this, we can start with the slope-intercept form of a linear equation:
y = mx + b
where m is the slope and b is the y-intercept.
In the case of the graph in the image, we know that the slope is -2 and the y-intercept is 4. So, we can plug these values into the slope-intercept form to get the equation:
y = -2x + 4
We can also check this answer by looking at the graph. The y-intercept is the point where the line crosses the y-axis. So, the y-intercept of the line in the image is (0, 4). This is consistent with the equation y = -2x + 4, which has a y-intercept of 4.
Here is a 200-word explanation of why the answer is y = -2x + 4:
A linear equation is an equation of the form y = mx + b, where m is the slope and b is the y-intercept. The slope of a line is a measure of how steep the line is, and the y-intercept is the point where the line crosses the y-axis.
The graph in the image shows a line with a slope of -2 and a y-intercept of 4. This means that the equation of the line is y = -2x + 4.
To see this, we can start by looking at the slope. The slope of a line is calculated by taking the change in y over the change in x. In the case of the line in the image, the change in y is -2 from (0, 4) to (1, 2), and the change in x is 1. So, the slope of the line is -2/1 = -2.
We can also see that the y-intercept of the line is 4. This is because the line crosses the y-axis at the point (0, 4).
Finally, we can check our answer by plugging the values for m and b into the slope-intercept form of a linear equation:
y = mx + b
y = -2x + 4
This gives us the same equation as the one in the image, so we know that our answer is correct.