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.
