A line passes through the point (–3, 4) and its y-intercept is (0, –2). What is the equation of the line that is parallel to the given line and passes through the point (–5, 2)?
Accepted Solution
A:
Answer:y = - 2x - 8Step-by-step explanation:The equation of a line in slope- intercept form isy = mx + c ( m is the slope and c the y- intercept )Calculate m using the slope formulam = (y₂ - y₁ ) / (x₂ - x₁ )with (x₁, y₁ ) = (- 3, 4) and (x₂, y₂ ) = (0, - 2) ← 2 points on the linem = [tex]\frac{-2-4}{0+3}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2• Parallel lines have equal slopes, hence slope of parallel line = - 2, thusy = - 2x + c ← partial equation of parallel lineTo find c substitute (- 5, 2) into the partial equation2 = 10 + c ⇒ c = 2 - 10 = - 8y = - 2x - 8 ← equation of parallel line