Answer:
y = 3x + 3
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
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From the table we have :
x = 1 → y = 6
x = 2 → y = 9
x = 3 → y = 12
x = 4 → y = 15
Calculate the slope (choice any two pairs, and calculate the slope):
(1, 6), (2, 9)
[tex]m=\dfrac{9-6}{2-1}=\dfrac{3}{1}=3[/tex]
We have the equation:
[tex]y=3x+b[/tex]
Put the coordinates of the point (1, 6) to the equation, and solve it for b:
[tex]6=3(1)+b[/tex]
[tex]6=3+b[/tex] subtract 3 from both sides
[tex]3=b\to b=3[/tex]
Finally:
[tex]y=3x+3[/tex]
