Answer:
1. x - 1 = 4(y + 6); passes through (1, -6) and (4, 6)
2. x - 4 = 6(y + 1); passes through (4, -1) & has slope 6
Explanation:
1. Finding the equation of the line in point-slope form that passes through (1, -6) and (4, 6):
General equation of the point-slope form:
The general equation of the point-slope form of a line is given by:
y - y1 = m(x - x1), where
- m is the slope,
- and (x1, y1) is any point on the line.
Finding the slope (m) using the slope formula:
Given two points on a line, we can find its slope using the slope formula, which is given by:
m = (y2 - y1) / (x2 - x1), where
- m is the slope,
- (x1, y1) is one point on the line,
- and (x2, y2) is another point.
Thus, we can find the slope (m) by substituting (1, -6) for (x1, y1) and (4, 6) for (x2, y2) in the slope formula:
m = (6 - (-6)) / (4 - 1)
m = (6 + 6) / (3)
m = 12 / 3
m = 4
Thus, the slope of the line is 4.
Writing the equation of the line in point-slope form:
Now, we can find the equation of the line in point-slope form by substituting (1, -6) for (x1, y1) and 4 for m in the point-slope general equation:
x - 1 = 4(y - (-6))
x - 1 = 4(y + 6)
Therefore, x - 1 = 4(y + 6) is the equation of the line in point-slope form that passes through (1, -6) and (4, 6).
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2. Finding the equation of the line that passes through (4, -1) and has slope 6:
Finally, we can find the equation of the line in point-slope form that passes through (1, -6) and has slope 6 by substituting (1, -6) for (x1, y1) and 6 for m in the point-slope general equation:
x - 4 = 6(y - (-1))
x - 4 = 6(y + 1)
Therefore, x - 4 = 6(y + 1) is the equation of the line in point-slope form that passes through (4, -1).