Resource Lesson
Properties of Lines
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To calculate the
slope
,
m
, of a line passing through two points, (x
_{1}
, y
_{1}
) and (x
_{2}
, y
_{2}
) use this formula:
slope = Δy / Δx
slope = (y
_{2}
- y
_{1}
) / (x
_{2}
- x
_{1}
)
To calculate the line's
y-axis intercept
,
b
, use the formula,
y = mx + b
and substitute in the values of the slope,
m
, along with the coordinates of one data point - either (x
_{1}
, y
_{1}
) or (x
_{2}
, y
_{2}
). You can then solve for
b
, as it will be the only variable remaining in the equation.
The equation of the line can then be written as
y
=
m
x
+
b
once you substitute in your exact values for the line's slope and y-axis intercept.
Once you know the line's equation you can determine the coordinates of any of its other points.
Interpolation
means to use the equation of the line to determine the coordinate of a point that would fall inside the domain or range of the graph.
Extrapolation
means to use the equation of the line to determine the coordinate of a point that would fall outside the domain or range displayed on the graph.
Refer to the following information for the next ten questions.
A graph of Mass (grams) vs Volume (cm
^{3}
) for two samples composed of the same metal is linear. Two data points having the coordinates (2, 18) and (5, 42) have been plotted.
(1) Which variable belongs on the x-axis?
(2) State the coordinates of two grid-points that fall on this line.
(3) Solve for the numerical value of the slope?
(4) What are the dimensions (units of measurement) for this slope?
(5) What physical quantity is represented by the slope?
(6) Solve for the line's y-axis intercept.
(7) Does this value seem reasonable according to your graph? Explain?
(8) What is the equation of this line (please use correct variables: not x and y)?
(9) Interpolate a value for the mass present in a sample if its volume equals 3.5 cm
^{3}
.
(10) Extrapolate the volume required for a sample whose mass equals 100 grams.
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