Question

Write an equation in slope-intercept form of the line that passes through (7,2) and (2, 12).​

Answer 1

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

$y = mx + b$

Where:

m: It's the slope

b: It is the cut-off point with the y axis

$m = \frac {y2-y1} {x2-x1}$

We have the following points:

$(x1, y1): (7,2)\\(x2, y2): (2,12)$

Substituting:

$m = \frac {12-2} {2-7} = \frac {10} {- 5} = - 2$

Thus, the equation is of the form:

$y = -2x + b$

We substitute one of the points to find the cut point "b":

$2 = -2 (7) + b\\2 = -14 + b\\2 + 14 = b\\16 = b$

Thus, the equation is:

$y = -2x + 16$

Answer:

$y = -2x + 16$