a line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation ( y =…

a line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation ( y = -\frac{5}{3}(x - 2) ). which equations also represent this line? select three options.\n( square y = -\frac{5}{3}x - 2 )\n( square y = -\frac{5}{3}x + \frac{10}{3} )\n( square 3y = -5x + 10 )\n( square 3x + 15y = 30 )\n( square 5x + 3y = 10 )

a line that passes through the points (-4, 10) and (-1, 5) can be represented by the equation ( y = -\frac{5}{3}(x - 2) ). which equations also represent this line? select three options.\n( square y = -\frac{5}{3}x - 2 )\n( square y = -\frac{5}{3}x + \frac{10}{3} )\n( square 3y = -5x + 10 )\n( square 3x + 15y = 30 )\n( square 5x + 3y = 10 )

Answer

Explanation:

Step1: Expand the given equation

Expand (y = -\frac{5}{3}(x - 2)) using the distributive property (a(b - c)=ab - ac). [ \begin{align*} y&=-\frac{5}{3}x+\frac{10}{3}\ \end{align*} ] Multiply through by (3) to get (3y=-5x + 10), and then rewrite it as (5x+3y = 10) (by adding (5x) to both sides).

Step2: Check each option

  • For (y=-\frac{5}{3}x - 2): The (y) - intercept (-2\neq\frac{10}{3}), so this is incorrect.
  • For (y = -\frac{5}{3}x+\frac{10}{3}): This is the expanded form of the given point - slope equation, so it is correct.
  • For (3y=-5x + 10): This is obtained by multiplying (y = -\frac{5}{3}x+\frac{10}{3}) by (3), so it is correct.
  • For (3x + 15y=30): Divide by (3) gives (x + 5y = 10), then (y=-\frac{1}{5}x+2). The slope (-\frac{1}{5}\neq-\frac{5}{3}), so it is incorrect.
  • For (5x+3y = 10): This is equivalent to (3y=-5x + 10) (by subtracting (5x) from both sides) and (y = -\frac{5}{3}x+\frac{10}{3}) (dividing by (3)), so it is correct.

Answer:

B. (y = -\frac{5}{3}x+\frac{10}{3}), C. (3y=-5x + 10), E. (5x+3y = 10)