As we can see based on the graph, it is a linear relation. Therefore, the equation will have the form:
[tex]y=mx+b[/tex]
where m is the slope and b is the y-intercept.
To know those values, we have to choose two coordinates of the graph given. As an example, I will choose:
• Point 1: ,( -1, 4 )
,
• Point 2: ,( 2, -2 )
However, you can choose any two coordinates you want to as long as they are part of the line.
Procedure:
0. Calculating the slope:
[tex]m=\frac{y_2-y_1}{x_{2_{}}-x_1}[/tex]
Replacing the values with the coordinates chosen:
[tex]m=\frac{(-2)-(4)_{}}{(2)_{}_{}-(-1)_{}}[/tex][tex]m=\frac{-2-4_{}}{2_{}+1}=\frac{-6}{3}[/tex][tex]m=-2[/tex]
With the slope calculated, we can now proceed to calculate the intersection with y-axis by replacing one of the points in the equation:
[tex]y=mx+b[/tex]
Replacing the values of Point 1:
[tex]4=-2(-1)+b[/tex][tex]4=2+b[/tex][tex]b=4-2[/tex][tex]b=2[/tex]
Answer: B.
[tex]y=-2x+2[/tex]
