find the x - and y - intercepts of each equation, then graph the line.\n13. $y=-6x - 5$\n14…

find the x - and y - intercepts of each equation, then graph the line.\n13. $y=-6x - 5$\n14. $\frac{9}{4}x-\frac{1}{2}y=-3$\n15. which equations are parallel to the line $-3x - 6y = 30$? check all that apply.\n$2x - y = 15$ $y=-3x + 1$ $4y = 20 - 2x$ $5x + 10y = 10$ $x = 18 - 2y$ $6 - 2y = 4x$\n16. give an example of a linear equation that is perpendicular to $y = 5$.\nwrite the equation of the line in slope - intercept form with the given info.\n17. passes through $(-2,6)$ with a slope of $-\frac{1}{4}$\n18. passes through $(2,-2)$ and $(-3,-17)$

find the x - and y - intercepts of each equation, then graph the line.\n13. $y=-6x - 5$\n14. $\frac{9}{4}x-\frac{1}{2}y=-3$\n15. which equations are parallel to the line $-3x - 6y = 30$? check all that apply.\n$2x - y = 15$ $y=-3x + 1$ $4y = 20 - 2x$ $5x + 10y = 10$ $x = 18 - 2y$ $6 - 2y = 4x$\n16. give an example of a linear equation that is perpendicular to $y = 5$.\nwrite the equation of the line in slope - intercept form with the given info.\n17. passes through $(-2,6)$ with a slope of $-\frac{1}{4}$\n18. passes through $(2,-2)$ and $(-3,-17)$

Answer

Explanation:

Step1: Find x - intercept of (y=-6x - 5)

Set (y = 0), then (0=-6x - 5), so (6x=-5), and (x=-\frac{5}{6}).

Step2: Find y - intercept of (y=-6x - 5)

Set (x = 0), then (y=-6\times0 - 5=-5).

Step3: Find x - intercept of (\frac{9}{4}x-\frac{1}{2}y=-3)

Set (y = 0), then (\frac{9}{4}x=-3), so (x=-\frac{4}{3}).

Step4: Find y - intercept of (\frac{9}{4}x-\frac{1}{2}y=-3)

Set (x = 0), then (-\frac{1}{2}y=-3), so (y = 6).

Step5: Rewrite (-3x-6y = 30) in slope - intercept form

(-6y=3x + 30), (y=-\frac{1}{2}x - 5), slope (m=-\frac{1}{2}).

  • For (2x-y=15), (y = 2x-15), slope (m = 2).
  • For (y=-3x + 1), slope (m=-3).
  • For (4y=20 - 2x), (y=-\frac{1}{2}x + 5), slope (m=-\frac{1}{2}).
  • For (5x + 10y=10), (10y=-5x + 10), (y=-\frac{1}{2}x+1), slope (m=-\frac{1}{2}).
  • For (x=18 - 2y), (2y=-x + 18), (y=-\frac{1}{2}x + 9), slope (m=-\frac{1}{2}).
  • For (6-2y=4x), (-2y=4x - 6), (y=-2x + 3), slope (m=-2).

Step6: Equation perpendicular to (y = 5)

(y = 5) is a horizontal line, a perpendicular line is a vertical line, e.g., (x = 1).

Step7: Write equation for line passing through ((-2,6)) with slope (-\frac{1}{4})

Using (y - y_1=m(x - x_1)), (y-6=-\frac{1}{4}(x + 2)), (y-6=-\frac{1}{4}x-\frac{1}{2}), (y=-\frac{1}{4}x+\frac{11}{2}).

Step8: Find slope for line passing through ((2,-2)) and ((-3,-17))

(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-17+2}{-3 - 2}=\frac{-15}{-5}=3). Using (y - y_1=m(x - x_1)) with ((x_1,y_1)=(2,-2)), (y + 2=3(x - 2)), (y=3x-8).

Answer:

  1. x - int: ((-\frac{5}{6},0)), y - int: ((0,-5))
  2. x - int: ((-\frac{4}{3},0)), y - int: ((0,6))
  3. (4y=20 - 2x), (5x + 10y=10), (x=18 - 2y)
  4. (x = 1) (any vertical line equation)
  5. (y=-\frac{1}{4}x+\frac{11}{2})
  6. (y=3x-8)