For Exercises 29–36, use the point-slope formula to write an equation of the line given the following information. (See Examples 3–4.) The line passes through the point ( 4 , − 1 ) and is parallel to the line y = 3 x + 1 .
For Exercises 29–36, use the point-slope formula to write an equation of the line given the following information. (See Examples 3–4.) The line passes through the point ( 4 , − 1 ) and is parallel to the line y = 3 x + 1 .
Solution Summary: The author calculates the equation of the line passing through (4,-1) and parallel to line y=3x+1 using point-slope formula.
For Exercises 29–36, use the point-slope formula to write an equation of the line given the following information.(See Examples 3–4.)
The line passes through the point
(
4
,
−
1
)
and is parallel to the line
y
=
3
x
+
1
.
Formula Formula Point-slope equation: The point-slope equation of a line passing through the point (x 1 , y 1 ) with slope m , is given by the following formula: y - y 1 = m x - x 1 Example: The point-slope equation of a line passing through (2, -6) with slope 5 is given by: y - (-6) = 5(x - 2) y + 6 = 5(x - 2)
In Exercises 25–27, use the given conditions to write an equation
for each line in point-slope form and slope-intercept form.
25. Passing through (-1, –3) and (4, 2)
26. Passing through (-2, 3) and perpendicular to the line
whose equation is y = -3x – 4
27. Passing through (6, -4) and parallel to the line
whose equation is x + 2y = 5
For Exercises 25–36, determine the slope of the line passing through the given points. (See Example 2)
25. (4, –7) and (2, – 1)
26. (-3, –8) and (4, 6)
27. (17, 9) and (42, –6)
28. (-9, 4) and (-1, –6)
29. (30, –52) and (-22, –39)
30. (- 100, -16) and (84, 30)
31. (2.6, 4.1) аnd (9.5, —3.7)
32. (8.5, 6.2) аnd (-5.1, 7.9)
33.
6) and
35. (3 V6, 2V5) and (V6, V5)
36. (2VIT, –3V3) and (VTI, -5V3)
34.
-3,
and
4,
10
Write the equation for the line through the points (-2, 8)
and (7, –10) in the form y = m(x – xo) + yo where m is the
slope of the line and (xo, yo) is a point that it passes through.
This is sometimes referred to as the point-slope form of the
line.
y =
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