Question on: JAMB Mathematics - 2024
Find the equation of the line through the points (5, 7) parallel to the line 7x + 5y = 12.
5x + 7y = 120
7x + 5y = 70
x + y = 7
15x + 17y = 90
We are given the equation of a line: \(7x + 5y = 12\), and we need to find the equation of a line passing through the point (5, 7) and parallel to this line. Parallel lines have the same slope. To find the slope of the given line, we rewrite it in slope-intercept form:
\(5y = -7x + 12\)
\(y = -\frac{7}{5}x + \frac{12}{5}\)
The slope is -\(7/5\). Using the point-slope form:
\(y - y_1 = m(x - x_1)\)
Substitute the point (5,7) and slope -7/5:
\(y - 7 = -\frac{7}{5}(x - 5)\)
Expand and simplify:
\(y - 7 = -\frac{7}{5}x + 7\)
\(y = -\frac{7}{5}x + 14\)
Multiply through by 5:
5y = -7x + 70
Simplified: 7x + 5y = 70
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