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Question
Find the equation of a line that has y-intercept −4 and is parallel to the line joining (2, −5) and (1, 2).
Solution
Let m be the slope of the required line.
c = y-intercept = -4
It is given that the required line is parallel to the line joining the points (2, −5) and (1, 2).
\[\therefore m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 + 5}{1 - 2} = - 7\]
Substituting the values of m and c in y = mx + c, we get, y = \[-\]7x \[-\] 4
\[\Rightarrow\] 7x + y + 4 = 0
Hence, the equation of the required line is 7x + y + 4 = 0
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