Answer:
Question 1: Function 2
Question 2: Function 4
Question 3: Function 4
Step-by-step explanation:
y-intercepts
A y-intercept is a y-value given when x is 0. When given the equation of a linear function, y = mx+b, the value b is characterized as the y-intercept. According to each function:
- Function 1 has a y value of 2 when x is 0, therefore a y-intercept of 2.
- Function 2 has a y value of 4 when x is 0, therefore a y-intercept of 4.
- In function 3, given the equation in the form y = mx+b, the b value being the y- intercept appears to be -5.
- In function 4, it just points out that the y- intercept is -3.
So amongst the four given functions, it would seem that function 2 has the greatest y-intercept with a value of 4.
Slope and Steepness
When calculating how steep a function is, you are analyzing the slope. The more steep a function is, the higher the slope will be and vise versa. To find out which one is the least steep i.e. lowest slope, you will need to find the equation of each function.
Function 1
In order to find the equation of the line given the graph, you would take two coordinates and apply the formula
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
where y2 and y1 are the y-values of the second and first coordinate respectively, and x2 and x1 are the x-values of the second and first coordinate respectively.
On the graph, we were kindly given two values to find the equation, (0,2) and (1,3).
Doesn't matter which coordinate is first and the other is second. Lets take (1.3) as coordinate 2 and (0,2) as coordinate 1.
With that in mind
x1 = 0
x2 = 1
y1 = 2
y2 = 3
Now simply plug it in the formula
[tex]\frac{3-2}{1-0} = \frac{1}{1} = 1 = m[/tex]
Therefore the slope here is 1.
To find b, it was mentionned earlier that for function 1, the y-intercept is 2.
So the equation is y = x + 2
Function 2
When given the table, it is the same process as the graph, you take two coordinates and apply the slope formula.
lets take (-1,6) and (0,4)
x1 = -1
x2 = 0
y1 = 6
y2 = 4
Now plug the values to the formula
[tex]\frac{4-6}{0-(-1)} = \frac{-2}{1} = -2[/tex]
Like said before, the y-intercept of the second function is 4. Therefore, the equation of this function is -2x+4 = y.
Function 3
y = 3x-5
Function 4
Since the slope is -5 and the y-intercept is -3, the equation will therefore be represented as -5x +3
Now that we got all the equations of the different functions, what we really need from those functions are the slopes. Each function respectively has the slope 1, -2, 3 and -5. Since -5 is the smallest number, function 4 has the lowest steep.
Slope less than -3
Amongst the different slopes found in the previous questions, 05 is the only number that is lower than -3. Therefore, function 4 is the only function that has a slope less than -3, with a slope of -5.
