Drawing a line on a graph can be done by plotting the ordered pair of values of the line's equation
2. Please find the drawing of the line passing through C and parallel to line AB
3. Yes, the line will eventually pass through the point E(18, 8)
Reason:
2. The coordinates of the point A is (-6, -1)
The coordinates of the point B is (6, -9)
The coordinates of the point C is (3, 2)
The slope, m, of the line AB, is therefore;
- [tex]m = \dfrac{-9 - (-1)}{(6 - (-6))} = -\dfrac{8}{12} = -\dfrac{2}{3}[/tex]
The slope, m₁ of a line parallel to AB and passing through point C, is therefore;
- [tex]m_1 = m = -\dfrac{2}{3}[/tex]
The equation of the line is therefore;
[tex]y - 2 = -\dfrac{2}{3} \times (x - 3)[/tex]
- [tex]y = -\dfrac{2}{3} \times (x - 3) + 2[/tex]
With the above equation, the line parallel to line AB is drawn using a spreadsheet application (MS Excel) as shown in the attached diagram
3. To verify if the line will eventually pass through point E(18, -8), the value of x = (18) is plugged into the equation to find the resulting y-value at the given point
At x = 18, we have;
[tex]y = -\dfrac{2}{3} \times (18 - 3) + 2 = -8[/tex]
y = -8
Therefore, from the equation (18, -8) is an ordered pair on the line, therefore
- Yes, the line eventually pass through point E(-18, 8)
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