1. Function Q and function R are both linear functions. Function Q has an x-intercept at (4,0), and the slope is 1/4. Function R is represented by the table.
x y
-4 14
3 0
5 -4
Which statement is true?
A. Function Q has a larger y-intercept and a less steep slope than function R
B. Function Q has a larger y-intercept and a steeper slope than function R
C. Function Q has a smaller y-intercept and a less steep slope than function R
D. Function Q has a smaller y-intercept and a steeper slope than function R
BTW, I really need help! This is for a really important benchmark, and it's a little overdue.
So you are going to make me even more late by not helping, what you are here for?
I do not know how to help you. A math tutor should be around in an hour or two.
Ms. Sue, in the future, please don't respond, especially telling me to do it on my own if you don't know. And I don't need a tutor. Especially this late. Thanks, tho.
If you don't need a tutor, why did you post on Jiskha?
Because not everyone on here is a tutor
Look, can someone just answer my question???
To determine which statement is true, we need to compare the characteristics of function Q and function R.
First, let's analyze function Q. We are given that function Q is a linear function with an x-intercept at (4,0) and a slope of 1/4. The x-intercept is the point where the function intersects the x-axis, which means when x=4, y=0. The slope of 1/4 indicates that for every increase in x by 1 unit, the corresponding y-value increases by 1/4 units.
Now, let's analyze function R using the given table. The table provides the corresponding y-values for different x-values. By examining the given points, we can create two coordinate pairs: (3,0) and (5,-4).
To find the slope of function R, we can use the formula: slope = (change in y)/(change in x). Taking (3,0) as the first point and (5,-4) as the second point, we have (0-(-4))/(3-5) = 4/(-2) = -2.
Comparing the slopes of function Q and function R, we see that the slope of function Q (1/4) is positive, while the slope of function R (-2) is negative. Therefore, we can conclude that function Q has a steeper slope than function R.
Next, let's compare the y-intercepts. We are not given the y-intercept of function Q, but we can find it by substituting the x-coordinate (4) and the slope (1/4) into the equation of a line: y = mx + b, where m is the slope and b is the y-intercept.
0 = (1/4)(4) + b
0 = 1 + b
b = -1
So, the y-intercept of function Q is -1.
Now, let's look at the given points for function R. None of these points lie on the y-axis, so we cannot directly determine the y-intercept from the table. However, we know that the y-intercept is the point where the function crosses the y-axis, which occurs when x=0. To find the y-intercept, we need to determine the corresponding y-value when x=0.
Substituting x=0 into the equation of a line: y = mx + b, where m is the slope and b is the y-intercept, we have:
y = (-2)(0) + b
y = b
Since b represents the y-intercept, we can infer that function R has a y-intercept of 14. This is obtained from the table, where the y-value is 14 when x=-4.
Now, comparing the y-intercepts, we find that function Q has a smaller y-intercept (-1) and function R has a larger y-intercept (14) than function Q.
Considering the information we have gathered, the correct statement is:
C. Function Q has a smaller y-intercept and a less steep slope than function R
If it's that important, you'd better figure out how to do it yourself.
Function Q:
(4, 0), m = 1/4.
Y = mx + b.
0 = (1/4)4 + b,
b = -1 = y-int.
Eq: Y = (1/4)x - 1.
Function R:
(x, y): (-4, 14), (3, 0), (5, -4).
m = (0-14)/(3-(-4)) = -14/7 = --2.
Y = mx + b,
14 = -2*(-4) + b.
b = 6 = y-int.
Eq: Y = -2x + 6.