Question

The line that contains the point q( 1, -2) and is parallel to the line whose equation is y - 4 = 2/3 (x - 3)

Answer 1

The equation of the line that contains the point Q(1, -2) and is parallel to the line y - 4 = 2/3 (x - 3) is y = 2/3x - 8/3.

Step-by-step explanation:

The student is asking how to find the equation of a line that passes through a given point, Q(1, -2), and is parallel to another given line, whose equation is in the point-slope form: y - 4 = ⅓(x - 3). The slope of the original line is 2/3, and since parallel lines have the same slope, we can use this slope for the new line. The point-slope form of a line's equation is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. Substituting the slope and point Q into this formula, we get the equation of the new line: y - (-2) = ⅓(x - 1) or y + 2 = ⅓x - ⅓, which simplifies to the final equation: y = ⅓x - ⅓ - 2.

Answer 2

Hello:
equation is the line is : y = ax+b a is a slope
y = (2/3)x+b (same slope because lines are parallel)
passing through the point q(1;−2) : -2 =(2/3)(1)+b b=-8/3
y = (2/3)x-(8/3)