Question

The table shows the average bill totals for given numbers of diners at Simone’s restaurant. If the rate is constant and you graph this relationship with the number of people along the x-axis and bill amounts along the y-axis, which points will lie on the line you get?
Persons Bill Amount
1 ------------$40
2                  $80
7 -------------$280
9                  $360
11                  $440




A.(12, 460
B.(20, 800)
C.(24, 1,020
D.(27, 1,080)
E.(28, 1,110)

JUST FYI THERE IS MORE THAN ONE ANSWER
NEED HELP ASAP

Answer 1

Answer:

Option B and D are correct.

(20, 800) and (27, 1080) points lie on the graph y = 40x

Step-by-step explanation:

Point slope intercept form: The general form of linear equation is given by $y-y_1 = m(x-x_1)$ ,.....[1] where m is the slope of the line and a point on a line$(x_1, y_1)$.

From the given table:

Consider any two points i.e,

let A = (1, 40) and B = (2, 80)

First calculate slope(m);

$m = \frac{y_2-y_1}{x_2-x_1}$

Substitute the given points, we have;

$m = \frac{80-40}{2-1}=\frac{40}{1}$ = 40 which is constant.

Now, substitute the value of m and (1, 40) in [1] we get;

$y-40 = 40(x-1)$

Using distributive property; $a \cdot(b+c) = a\cdot b + a\cdot c$

$y-40 = 40x-40$

Add both sides 40 we get;

y = 40x;  where x represents the number of people and y represents the bill amount

We have to find which points lie on the graph y = 40 x;

Option A:

(12, 460)

substitute in the graph y = 40x

460 = 40(12)

460 = 480    False.

Option B:

(20, 800)

substitute in the graph y = 40x

800 = 40(20)

800= 800    True.

Option C:

(24, 1020)

substitute in the graph y = 40x

1020 = 40(24)

1020= 960    False.

Option D:

(27, 1080)

substitute in the graph y = 40x

1080 = 40(27)

1080=1080   True.

Option E:

(28, 1110)

substitute in the graph y = 40x

1110 = 40(28)

1110= 1120    False.

Therefore, the points which lie on the graph y= 40x are; (20, 800) and (27, 1080)

Answer 2

B and D are the correct answers