Question

A line contains the points (34, 12) and (32,48). What is the slope of the line in simplified form

Answer 1

slope = (y2-y1)/(x2-x1)
slope = (48-12)/(32-34)
slope =36/-2
slope =-18

Answer 2

Keywords:

Equation of the line, slope, interseption, points

For this case we have that the equation of the line of the slope-interseption form is given by the form y = mx + b. Where: "m" is the slope and "b" is the cut point with the "y" axis. The slope is given by the following equation:

$m = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}$, to find it, we need two points.

If we have:

$(x_ {1}, y_ {1}) = (34,12)\\(x_ {2}, y_ {2}) = (32,48)$

We substitute in the formula:

$m = \frac {48-12} {32-34}\\m = \frac {36} {- 2}\\m = -18$

So, the equation of the line is of the form: $y = -18x + b$

To find the cut point, substitute any of the points in the equation:

$12 = -18 (34) + b\\12 = -612 + b\\b = 612 + 12\\b = 624$

Thus, the equation of the line is of the form: $y = -18x + 624$

Answer:

The equation of the line is of the form: $y = -18x + 624$

Where "-18" is the slope and "624" is the cut point with the y-axis.