The equation in the table is linear because as the x values increase by 1, and y values increase by 3.
The general form of a linear equation is :
[tex]y\text{ = ax + b}[/tex]
where:
a is the slope and b is the intercept
The slope can be calculated using the fomula:
[tex]slope\text{ =}\frac{y_2-y_1}{x_2-x_1}\text{ }[/tex]
where (x1,y1) and (x2,y2) are two points on the table.
We can find two points on the table:
(6, 13) and (7, 16)
Hence, the slope:
[tex]\begin{gathered} \text{slope = }\frac{16-13}{7-6} \\ =\text{ 3} \end{gathered}[/tex]
The intercept is the value of y when the line cuts the y-axis.
Using the formula for slope and the point (0,y), we can find the intercept.
[tex]\begin{gathered} \frac{y-13}{0-6}=3 \\ -18\text{ = y-13} \\ y\text{ = -18 + 13} \\ =\text{ -5} \end{gathered}[/tex]
Hence, the required equation is:
[tex]y\text{ = 3x - 5}[/tex]
Answer:
y = 3x - 5
