Answer: [tex]y=3x+7[/tex]
Step-by-step explanation:
The complete exercise is attached.
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
The slope can be found with this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can pick the points on the given line:
[tex](1,10)\\(3,16)[/tex]
We can say that:
[tex]y_2=16\\y_1=10\\\\x_2=3\\x_1=1[/tex]
Then, substituting values into the formula, we get:
[tex]m=\frac{16-10}{3-1}=3[/tex]
Now we need to substitute the slope and the coordinates of one of the points into [tex]y=mx+b[/tex] and then solve for "b":
[tex]10=(3)(1)+b\\\\10-3=b\\\\b=7[/tex]
Therefore, the equation of this line in Slope-Intercept form, is:
[tex]y=3x+7[/tex]
