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 [tex]y-y_1 = m(x-x_1)[/tex] ,.....[1] where m is the slope of the line and a point on a line[tex](x_1, y_1)[/tex].
From the given table:
Consider any two points i.e,
let A = (1, 40) and B = (2, 80)
First calculate slope(m);
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute the given points, we have;
[tex]m = \frac{80-40}{2-1}=\frac{40}{1}[/tex] = 40 which is constant.
Now, substitute the value of m and (1, 40) in [1] we get;
[tex]y-40 = 40(x-1)[/tex]
Using distributive property; [tex]a \cdot(b+c) = a\cdot b + a\cdot c[/tex]
[tex]y-40 = 40x-40[/tex]
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)
