Step-by-step explanation:
3x - 2y = 12
Substituting y = 9, we find:
[tex]3x - 2 \times 9 = 12 \\ \therefore \: 3x - 18 = 12 \\ \therefore \: 3x = 12 + 18 \\ \therefore \: 3x = 30 \\ \therefore \: x = \frac{30}{3} \\ \therefore \: x = 10 \\ \therefore \: A (...., 9) = A (10, \: 9) [/tex]
Similarly, solving for point B (4, __) =B (4, 0)
Coordinates of the the points A and B are (10, 9) and (4, 0) respectively and slope of the line will be [tex]\frac{3}{2}[/tex].
Equation of a line given in the question → 3x - 2y = 12
Points A and B lying on the line are,
Since, points A and B lie on the given line,
Satisfy the equation by the given points to find the unknown ordinates,
For A(h, 9),
3h - 2(9) = 12
3h = 12 + 18
h = [tex]\frac{30}{3}[/tex]
h = 10
For B(4, k),
3(4) - 2k = 12
2k = 12 - 12
k = 0
Therefore, coordinates of points A and B will be (10, 9) and (4, 0) respectively.
Slope of the line passing through A and B will be,
Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{9-0}{10-4}[/tex]
= [tex]\frac{9}{6}[/tex]
= [tex]\frac{3}{2}[/tex]
Hence, points A and B are (10, 9) and (4, 0) respectively and slope of the line will be [tex]\frac{3}{2}[/tex].
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