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A and B are the points (-7, 2) and (5, a) - Scottish Highers Maths - Question 11 - 2017
Question 11
A and B are the points (-7, 2) and (5, a). AB is parallel to the line with equation 3y - 2x = 4. Determine the value of a.
Worked Solution & Example Answer:A and B are the points (-7, 2) and (5, a) - Scottish Highers Maths - Question 11 - 2017
Step 1
Determine the gradient of the given line
Answer
To find the gradient of the line represented by the equation (3y - 2x = 4), we first rearrange it into slope-intercept form ((y = mx + b)):
- Rearranging gives: (3y = 2x + 4)
- Dividing through by 3 results in: (y = \frac{2}{3}x + \frac{4}{3})
Thus, the gradient (m) of the given line is (m = \frac{2}{3}.
Step 2
Step 3
Find a
Answer
The points A and B have coordinates A(-7, 2) and B(5, a). We use the formula for the gradient of a line through two points, which is given by:
(m_{AB} = \frac{y_2 - y_1}{x_2 - x_1})
Substituting the known values gives us:
(\frac{2 - a}{5 - (-7)} = \frac{2}{3})
This simplifies to (\frac{2 - a}{12} = \frac{2}{3}).
Cross-multiplying yields:
(3(2 - a) = 24)
(6 - 3a = 24)
(-3a = 24 - 6)
(-3a = 18)
Thus, (a = -6.