Find the equation of a line that has y – intercept – 4 and is para

1.	Find the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, – 5) and (1, 2).
Answer» Given, A line segment joining (2, – 5) and (1, 2) if it cuts off an intercept – 4 from y–axis. To Find: The equation of that line. Formula used: The equation of line is y = mx + C Explanation: Here, The required equation of line is y = mx + c Now, c = – 4 (Given) Slope of line joining (x₁ – x₂) and (y₁ – y₂) ,m = \(\frac{y_2-y_1}{x_2-x_1}\) So, Slope of line joining (2, – 5) and (1, 2), m = \(\frac{2-(-5)}{1-2}\) = \(\frac{7}{-1}\) Therefore, m = – 7 Now, The equation of line is y = mx + c y = –7x – 4 y + 7x + 4 = 0 Hence, The equation of line is y + 7x + 4 = 0.

Find the equation of a line that has y – intercept – 4 and is parallel to the line joining (2, – 5) and (1, 2).

Answer»

Given, A line segment joining (2, – 5) and (1, 2) if it cuts off an intercept – 4 from y–axis.

To Find: The equation of that line.

Formula used: The equation of line is y = mx + C

Explanation: Here, The required equation of line is y = mx + c

Now, c = – 4 (Given)

Slope of line joining (x₁ – x₂) and (y₁ – y₂) ,m = \(\frac{y_2-y_1}{x_2-x_1}\)

So, Slope of line joining (2, – 5) and (1, 2), m = \(\frac{2-(-5)}{1-2}\) = \(\frac{7}{-1}\)

Therefore, m = – 7

Now, The equation of line is y = mx + c

y = –7x – 4

y + 7x + 4 = 0

Hence, The equation of line is y + 7x + 4 = 0.