Points A (3; 5) and B (-3; 4) are given. Write the equation of the straight line passing through

Points A (3; 5) and B (-3; 4) are given. Write the equation of the straight line passing through the point C (-2,1) parallel to AB.

1. Let’s compose the equation of the straight line passing through points A and B:

A (3; 5);
B (-3; 4);
(y – 5) / (x – 3) = (4 – 5) / (- 3 – 3);
(y – 5) / (x – 3) = -1 / (- 6);
y – 5 = 1/6 * (x – 3);
y = 1/6 * x – 1/2 + 5;
y = 1/6 * x + 9/2.
Slope:

k = 1/6.

2. Parallel straight lines have equal slope, therefore, for the equation of a straight line parallel to AB and passing through point C, we get:

C (-2; 1);
y – 1 = k (x + 2);
y – 1 = 1/6 (x + 2);
y = 1/6 * x + 1/3 + 1;
y = 1/6 * x + 4/3.
Answer: y = 1/6 * x + 4/3.