Answer:
x + 31 = 2(y + 9)
Explanation:
General equation of the point-slope form:
The general equation of the point-slope form is given by:
x - x1 = m(y - y1), where:
- (x1, y1) are any point on a line,
- and m is the slope.
Finding the slope:
Given two points on a line, we can find the line's slope using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where:
- (x1, y1) is one point on the line,
- and (x2, y2) is another point on the line.
Thus, we can find the slope of the line by substituting (-9, -31) for (x1, y1) and (-2, -17) for (x2, y2) in the slope formula:
m = [-17 - (-31)] / [-2 - (-9)]
m = (-17 + 31) / (-2 + 9)
m = 14/7
m = 2
Thus, the slope of the line is 2.
Finding the equation of the line in point-slope form:
Now, we can find the equation of the line in point-slope form by substituting (-9, -31) for (x1, y1) and 2 for m in the general equation of the point-slope form:
x - (-31) = 2(y - (-9))
x + 31 = 2(y + 9)
Therefore, x + 31 = 2(y + 9) is the equation of the line in point-slope form, where (-9, -31) and (-2, -17) both lie on the line.