For Exercises 17–22, use the point-slope formula to write an equation of the line given the following information. (See Example 2.) The line passes through the points ( 4.7 , − 2.2 ) and ( − 0.3 , 6.8 ) .
For Exercises 17–22, use the point-slope formula to write an equation of the line given the following information. (See Example 2.) The line passes through the points ( 4.7 , − 2.2 ) and ( − 0.3 , 6.8 ) .
Solution Summary: The author calculates the equation of the line passing through the points using the point-slope formula.
For Exercises 17–22, use the point-slope formula to write an equation of the line given the following information. (See Example 2.)
The line passes through the points
(
4.7
,
−
2.2
)
and
(
−
0.3
,
6.8
)
.
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)
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
Exercises 83–86: The table lists data that are exactly linear.
a. Find the slope-intercept form of the line that passes through these
data points.
b. Predict y when x = -2.7 and 6.3. Decide if these calculations
involve interpolation or extrapolation.
-3
-2
-1
1
83.
y
-7.7
-6.2
-4.7
-3.2
-1.7
In Exercises 105–108, use a graphing utility to graph each linear
function. Then use the TRACE feature to trace along the
line and find the coordinates of two points. Use these points to
compute the line's slope. Check your result by using the
coefficient of x in the line's equation.
105. y = 2x + 4
106. y = -3x + 6
1
107. f(x) =
-X-
2
3
108. f(x) = 7*
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