Question

What is the function rule for the line?

Answer 1

For this case we have that the equation of a line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We can find the slope using two points that cross the line.

$(x1, y1) :( 1,2)\\(x2, y2) :( 2,6)\\m = \frac {y2-y1} {x2-x1} = \frac {6-2} {2-1} = \frac {4} {1} = 4$

Thus, the equation is of the form:

$y = 4x + b$

We substitute a point to find "b":

$2 = 4 (1) + b\\2 = 4 + b\\b = 2-4 = -2$

Finally, the equation is:

$y = 4x-2$

Answer:

$y = 4x-2$