find the slope form and with complete solution
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1. (12,-18) and (-5,-18)
The slope of a line passing through two points (x1,y1) and (x2,y2) is given by:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values we get:
slope = (-18 - (-18)) / (-5 - 12) = 0 / -17 = 0
The slope of the line passing through (12,-18) and (-5,-18) is zero. Since the y-coordinate is constant, the line is a horizontal line. The equation of the line in slope-intercept form is:
y = -18
2. (3, -20) and (5, 8)
The slope of the line passing through the two points is:
slope = (8 - (-20)) / (5 - 3) = 28 / 2 = 14
Using the point-slope form of the equation of a line, we can write:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Choosing (3, -20) as the point we get:
y - (-20) = 14(x - 3)
y + 20 = 14x - 42
y = 14x - 62
The equation of the line in slope-intercept form is y = 14x - 62.
3. (15,8) and (-17, 9)
The slope of the line passing through the two points is:
slope = (9 - 8) / (-17 - 15) = 1 / -32
Using the point-slope form of the equation of a line, we can write:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Choosing (15,8) as the point we get:
y - 8 = (1/-32)(x - 15)
y = -(1/32)x + (17/2)
The equation of the line in slope-intercept form is y = -(1/32)x + (17/2).
4. (-19, 12) and (-9, 1)
The slope of the line passing through the two points is:
slope = (1 - 12) / (-9 - (-19)) = -11 / 10
Using the point-slope form of the equation of a line, we can write:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is a point on the line. Choosing (-19, 12) as the point we get:
y - 12 = (-11/10)(x - (-19))
y = (-11/10)x + (208/10)
The equation of the line in slope-intercept form is y = (-11/10)x + (208/10) or y = (-11/10)x + 20.8.