Given Function A with points (–5, –2), (–5, 7) and Function B with points (7, –5), (–2, –5) represent linear functions, thus:
Function A has an undefined slope: no slope
Equation for line A would be: x = -5
Function B has a slope value of: 0.
Equation for line B is: y = -5
Recall:
- Slope-intercept form is for a vertical line: x = a number on the x-axis
- Slope-intercept form is for a horizontal line: y = a number on the y-axis
Thus:
Linear Function A with the points (–5, –2), (–5, 7):
[tex]Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 -(-2)}{-5 -(-5)} \\\\[/tex]
[tex]m = \frac{9}{0}[/tex] (can't divide. Undefined)
- Function A therefore has no slope (undefined).
- A line with no slope is a vertical line.
The equation for function A will therefore be written as: x = -5
- -5 is where the vertical line intersects the x-axis.
Linear Function B with the points (7, –5), (–2, –5):
[tex]Slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 -(-5)}{-2 - 7} \\\\[/tex]
[tex]m = \frac{0}{-9} = 0[/tex]
- A slope value of 0 means the line of the linear equation is an horizontal line.
The equation for function A will be written as: y = -5
- -5 is where the horizontal line intersects the y-axis.
In summary, given Function A with points (–5, –2), (–5, 7) and Function B with points (7, –5), (–2, –5) represent linear functions, thus:
Function A has an undefined slope: no slope
Equation for line A would be: x = -5
Function B has a slope value of: 0.
Equation for line B is: y = -5
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