write an equation of the line in point slope form that passes through the two given points.(-2,15),(9,-18).Please explain
use the two-point form:
(y-15)/(x+2) = (-18-15)/(9 + 2)
or
(y-15) = -3(x+2)
Thanks for the help
To write an equation of a line in point-slope form, we need two points on the line. The given points are (-2, 15) and (9, -18).
1. Determine the slope (m):
The slope, denoted by m, represents the rate at which the line is rising or falling. It can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
By substituting the coordinates of the given points, we can find the slope:
m = (-18 - 15) / (9 - (-2))
m = (-18 - 15) / (9 + 2)
m = (-33) / (11)
m = -3
So, the slope of the line is -3.
2. Choose one point and substitute its coordinates into the point-slope form:
Since we have the slope (m) and two points, we can select either of the points and substitute its coordinates in the point-slope form:
y - y1 = m(x - x1)
Let's use the first point (-2, 15):
y - 15 = -3(x - (-2))
y - 15 = -3(x + 2)
Simplifying the equation further:
y - 15 = -3x - 6
3. If required, rearrange the equation into a desired form:
The equation is already in the point-slope form. However, if you would like to convert it into slope-intercept form (y = mx + b), you can rearrange the equation:
y - 15 = -3x - 6
y = -3x - 6 + 15
y = -3x + 9
Therefore, the equation of the line in point-slope form that passes through the points (-2, 15) and (9, -18) is: y - 15 = -3(x + 2) or in slope-intercept form, y = -3x + 9.