Answer:
[tex]y=2x-6[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
From the table, consider the last two points:
[tex](4,2)\textrm{ and }(9,12)[/tex]
The equation of the line using two points is given as:
[tex]y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})[/tex]
Here, [tex](x_{1},y_{1})=(4,2)\textrm{ and }(x_{2},y_{2})=(9,12)[/tex]
[tex]y-2=\frac{12-2}{9-4}(x-4)\\ y-2=\frac{10}{5}(x-4)\\y-2=2(x-4)\\y-2=2x-8\\y=2x-8+2\\y=2x-6[/tex]
Therefore, the equation of the line in slope-intercept form is:
[tex]y=2x-6[/tex]
