(NOTE: many questions may ask you to put the equation in a certain format. This answer is assuming you can put it in slope-intercept form.)
Answer:
y= -3x-3
Explanation:
1) A handy way to write an equation from a graph is to use the slope-intercept form: y = mx + b. In this format, the "m" represents the slope - or the measure of the steepness of the graph (we'll get more into this in the next step). The "b" represent the y-intercept, or where the point in which the graph hits the y-axis. If you know what the slope and y-intercept is, it is very easy to create an equation!
2) So let's find the slope first. The slope of an equation is represented by
, or the change in the y from each point, going up or down, divided by the change of x, going from left to right. So, knowing this, we can take two points we see the line hit and count the change from the x and y values.
- Let's take the points (-1,0) and (0,-3).
- To find the rise, or the change in y, start from (-1,0) and count how many units it would take vertically to get to (0,-3). If you went down, then be sure to add a negative to the number of units you counted. To find the run, or change in x, do the same and count how many steps it would take horizontally to get to (0,-3) too. If you went left, then be sure to add a negative to the number of units you counted.
- So, if you did it correctly, you would get -3 as your rise and 1 as your run. Using the
equation, divide -3 by 1 and your slope is -3.
3) Now, let's find the y-intercept. This part is much easier: just look at the graph and find the point where the line hits the y-axis. In this case, it's (0,-3).
4) All you have to do now is plug the slope and y-intercept we found into y = mx + b. So, put the slope in the "m" place and remember to put the y-value of the y-intercept into the "b" place.
This should get you y= -3x - 3 as your answer!