Answer:
A: Function 1
B: Function 4
C: Function 2
Explanation A:
In order to solve this problem, you will have to find the slope for each function.
1st Function: For the first function, you will need to find 2 points, let's use (0, -4) and (1, 1). Remember slope is rise over run, so you would count the spaces from the first point to the second, it rises (y-axis) 5 points and runs (x-axis) 1 point. Which would give you 5/1 = 5. Function 1's slope is 5.
2nd Function: Same equation, rise over run, or y over x, so we need to find the pattern on each side. For the x-values, we can see starting from the first point that they increase by one, -2 to -1 to 0, and for the whole x-values, so 1 will be our run, since it is the x-value. For the rise, or y-values, we can see a pattern of -1 starting from the top going towards the bottom. Now, we can rise over run, -1/1 = -1
3rd Function: Slope is -4, as the equation is y = mx + b, and m stands for slope.
4th Function: Says slope is 2.
Now that we know all the slopes, we can see that Function 1's slope is the greatest.
Explanation B:
For this problem, we will have to find the y-intercept for all the functions, this means where the x-value is 0, so that the y-value will be right on the y-axis.
Function 1: We can see that the function intercepts the y-axis at (0, -4), it's y-intercept being -4.
Function 2: Where the x-value is 0, we can find the y-intercept, which is (0, 1). Making the y-intercept 1.
Function 3: Following the y = mx + b format, the b is the y-intercept, so it is -2.
Function 4: Gives you the y-intercept as 5.
In the end, the only function with a y-intercept greater than 4 is Function 4.
Explanation C:
Since we already know the y-intercepts from the previous problem, we only need to see which one is closest to 0. In this case, it would be Function 2 with a y-intercept at -1, only 1 unit off of 0, making it the closest.