Answer:
A & B
Step-by-step explanation:
See attachment for complete question
Given
[tex]y = \frac{1}{2}x[/tex]
Analyzing the given options
Option A:
[tex]6y = 3x[/tex]
Divide both sides by 6
[tex]\frac{6y}{6} = \frac{3x}{6}[/tex]
[tex]y = \frac{3x}{6}[/tex]
[tex]y = \frac{1}{2}x[/tex]
This is true for the given expression:
Option B:
From the graph:
x = 2, when y = 1
x = 4, when y = 2
Solving for the slope:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{2 -1}{4 - 2}[/tex]
[tex]m = \frac{1}{2}[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 1 = \frac{1}{2}(x - 2)[/tex]
[tex]y - 1 = \frac{1}{2}x - 1[/tex]
Add 1 to both sides
[tex]y - 1 +1 = \frac{1}{2}x - 1 + 1[/tex]
[tex]y = \frac{1}{2}x[/tex]
This is also true for the given expression.
Option C:
From the graph:
x = 2, when y = 4
x = 4, when y = 8
Solving for the slope:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8 - 4}{4 - 2}[/tex]
[tex]m = \frac{4}{2}[/tex]
[tex]m =2[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 4 = 2(x - 2)[/tex]
[tex]y - 4 = 2x - 4[/tex]
Add 4 to both sides
[tex]y - 4 + 4= 2x - 4 + 4[/tex]
[tex]y = 2x[/tex]
This isn't true for the given expression.
Option (D):
From the table:
x = 2, when y = 1
x = 4 when y = 3
Solving for the slope:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{3 - 1}{4 - 2}[/tex]
[tex]m = \frac{2}{2}[/tex]
[tex]m = 1[/tex]
The equation is then calculated as:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 1 = 1 * (x - 2)[/tex]
[tex]y - 1 = x - 2[/tex]
[tex]y = x - 2 +1[/tex]
[tex]y = x - 1[/tex]
This isn't true for the given expression.
