* Note: This was answered with the assumption that you are asking for both the slope and y-intercept in a y = mx + b formula, which matches the letter choice a. seen at the very bottom. I also probably could've explained this problem in a simpler, concise manner, but I wanted to show the appropriate formula that will work even if you have to find y = mx + b without a graph.
Equation should be:
y = 3x - 5
Reasoning for why:
I noticed the letter choice a. at the bottom of the question. It seems as though this problem would like a y = mx + b format, so that is what I will provide. Remember, m is the slope, and b is the y-intercept.
First things first, let's find the slope.
This time around, let's use the formula y2-y1/x2-x1. In order to do this, we must identify and pick two coordinate pairs (x, y). After observing the graph and its data, I came up with the two coordinates: (1, -2) and (2, 1).
Now that we have decided on the points, we can choose one of them for x1 and y1, and the other for x2 and y2. The 1's in the formula y2-y1/x2-x1 must be in the same coordinate pair; the same goes for the 2's in the formula. It doesn't particularly matter which one you label as which. Let's say (x1, y1) is (1, -2) and (x2, y2) is (2, 1). This means x1 is 1, x2 is 2, y1 is -2, and y2 is 1.
Alright - we have our values. Next, we simply insert them into the formula. For example, since y2 is 1, we simply replace the y2 in y2-y1/x2-x1 with its value: 1. After doing so, our new formula becomes 1-(-2)/2-1.
Let's calculate each side of our formula now! For 1-(-2), we have to deal with two negatives in a row (subtraction sign and the negative attached to -2). In this case, all we have to do is combine the two negatives to make a positive. In other words, 1-(-2) becomes 1+2. 1 + 2 = 3. So, 1-(-2) can be simplified as 3. The other side, 2-1, is a lot simpler. We simply subtract 1 from 2. 2 - 1 = 1. So, 2-1 can be simplified to 1.
After rewriting our slope formula with the new values, we have 3/1. The / is the same thing as division, or ÷. 3 ÷ 1 = 3. So, our slope is 3.
Okay, slope is out of the way. Keep that slope/m = 3 tucked away in your brain for later - we'll need it. As of right now, though, we now have to find the y-intercept.
This step is actually really easy. The y-intercept is literally just the value of y when the value of x is 0. On a graph, whatever value y is at when the line intercepts/touches the y-axis, that will be the y-intercept.
The line intercepts -5. Therefore, our y-intercept is -5.
Great! We've found our slope and our y-intercept. Our last step is to combine both of these values in the format I mentioned at the beginning. That is, the formula y = mx + b. As stated earlier, m stands for the slope, whilst b stands for the y-intercept. (By the way, y stands for y and x stands for x. These will not change into a specific value we must find for this question.) We've discovered that the slope is 3 and the y-intercept is -5. We can insert these to come up with y = 3x + (-5). Since adding a negative is the same thing as subtracting, our final formula is y = 3x - 5.
Therefore, the equation of the line shown in the graph, according to y = mx + b, is y = 3x - 5.
