Question

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

Answer 1

BTW, I really need help! This is for a really important benchmark, and it's a little overdue.

Answer 2

If it's that important, you'd better figure out how to do it yourself.

Answer 3

So you are going to make me even more late by not helping, what you are here for?

Answer 4

I do not know how to help you. A math tutor should be around in an hour or two.

Answer 5

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.

Answer 6

If you don't need a tutor, why did you post on Jiskha?

Answer 7

Because not everyone on here is a tutor

Answer 8

Look, can someone just answer my question???

Answer 9

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.

Answer 10

[AI-generated answer — Explain Bot]

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