Answer:
[tex]y = 3x + 5[/tex]
Step-by-step explanation:
The equation of a line in the pending intercept form has the following form:
[tex]y = mx + b[/tex]
Where m is the slope of the line and b is the intercept with the y axis.
If we know two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] that belong to the line then:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]b=y_1-mx_1[/tex]
In this case:
[tex](x_1, y_1)=(2,11)[/tex]
[tex](x_2, y_2)=(4,17)[/tex]
[tex]m=\frac{17-11}{4-2}[/tex]
[tex]m=\frac{6}{2}[/tex]
[tex]m=3[/tex]
[tex]b=11-3(2)[/tex]
[tex]b=11-6[/tex]
[tex]b=5[/tex]
Finally the equation is:
[tex]y = 3x + 5[/tex]
