Answer:
Options (1), (2), (3)
Step-by-step explanation:
Let the equation of the line is,
y = mx + b
Here m = slope of the line
b = y-intercept
Given line on the graph is passing through two points (-3, 0) and (0, 1).
Slope of this line will be,
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{1-0}{0+3}[/tex]
= [tex]\frac{1}{3}[/tex]
y-intercept of the line 'b' = 1
Equation of the line will be,
y = [tex]\frac{1}{3}x+1[/tex]
If the points given in the options satisfy the equation, they will be the solution of the line.
Option (1),
For (3, 2),
2 = [tex]\frac{3}{3}+1[/tex]
2 = 2
True.
(3, 2) is the solution.
Option (2)
For (21, 8),
8 = [tex]\frac{21}{3}+1[/tex]
8 = 8
True.
(21, 8) is the solution.
Option(3)
For (-15, -4),
-4 = [tex]\frac{-15}{3}+1[/tex]
-4 = -4
True.
(-15, -4) is the solution.
Option (4)
For (12, 9)
9 = [tex]\frac{12}{3}+1[/tex]
9 = 5
False
(12, 9) is not the solution.
Option (5)
For (-6, 1)
1 = [tex]\frac{-6}{3}+1[/tex]
1 = -1
False
(-6, 1) is not the solution.
Therefore, Options (1), (2), (3) are the solutions.
