Answer to Question #221060 in Algebra for ufzz

Question

Question no. 01: A. Solve the following Equations: a) |𝑥 − 6| = 3 b) |𝑥 − 4| = |−3𝑥 + 8| c) |2𝑥 + 4| = |5𝑥 + 2| B. Find the midpoint and distance of the line segment that connects the following points a) (0,3) and (4,7) b) (-9,6) and (-1, -2) c) (-4.5, -12.5) and (4.5, 13) Question no. 02: A. Find the slope, x-intercept and y-intercept form of the following equations a) 5x + 2y =-10 b) 13y -2x = 3 c) 25𝑦 + 31𝑥 − 18 = 10𝑦 d) −3𝑥 + 4𝑦 − 10 = 7𝑥 − 2𝑦 + 50 B. Find the slope of the line that connects the following points a) (0,3) and (4,7) b) (-9,6) and (-1, -2) C. Determine the slope-intercept form of a linear equation, given the listed attributes: a) Slope = -2 and y-intercept = (0,10) b) Slope = -3 and (4, -2) lies on line c) Slope = 0 and (2,4) lies on line d) (3, -2) and (-12,1) lies on line e) (20, 240) and (15,450) lies on line

Answer 1

1.

A.

a.

$$|x-6|=3$$

$$x-6=-3\ or\ x-6=3$$

$$x=3, 9$$

b.

$$|x-4|=|-3x+8|$$

$$x-4=-3x+8\ or\ x-4=3x-8$$

$$4x=12\ or\ 2x=4$$

$$x=2, 3$$

c.

$$|2x+4|=|5x+2|$$

$$2x+4=5x+2\ or\ 2x+4=-5x-2$$

$$3x=2\ or\ 7x=-6$$

$$x=-\dfrac{6}{7}, \dfrac{2}{3}$$

B.

a.

$$x=\dfrac{0+4}{2}=2, y=\dfrac{3+7}{2}=5$$

$$M(2, 5)$$

$$l=\sqrt{(4-0)^2+(7-3)^2}=4\sqrt{2}$$

b.

$$x=\dfrac{-9-1}{2}=-5, y=\dfrac{6-2}{2}=2$$

$$M(-5, 2)$$

$$l=\sqrt{(-1-(-9))^2+(-2-6)^2}=8\sqrt{2}$$

c.

$$x=\dfrac{-4.5+4.5}{2}=0, y=\dfrac{-12.5+13}{2}=0.25$$

$$M(0,0.25)$$

$$l=\sqrt{4.5-(-4.5))^2+(13-(-12.5))^2}=7.5\sqrt{13}$$

2.

A.

a.

$$5x+2y=-10$$

$$x=0:y=-5$$

y-intercept: $(0, -5)$

$$y=0:x=-2$$

x-intercept: $(-2, 0)$

$$y=-2.5(x+2)$$

slope $=-2.5$

$$y+5=-2.5x$$

b.

$$13y-2x=3$$

$$x=0:y=\dfrac{3}{13}$$

y-intercept: $(0, \dfrac{3}{13})$

$$y=0:x=-\dfrac{3}{2}$$

x-intercept: $(-\dfrac{3}{2}, 0)$

$$y=\dfrac{2}{13}(x+\dfrac{3}{2})$$

slope $=\dfrac{2}{13}$

$$y-\dfrac{3}{13}=\dfrac{2}{13}x$$

c.

$$25y+31x-18=0$$

$$x=0:y=\dfrac{18}{25}$$

y-intercept: $(0, \dfrac{18}{25})$

$$y=0:x=\dfrac{18}{31}$$

x-intercept: $(\dfrac{18}{31}, 0)$

$$y=-\dfrac{31}{25}(x-\dfrac{18}{31})$$

slope $=-\dfrac{31}{25}$

$$y-\dfrac{18}{25}=-\dfrac{31}{25}x$$

d.

$$-3x+4y-10=7x-2y+50$$

$$x=0:y=10$$

y-intercept: $(0, 10)$

$$y=0:x=-6$$

x-intercept: $(-6, 0)$

$$y=\dfrac{5}{3}(x-(-6))$$

slope $=\dfrac{5}{3}$

$$y-10=\dfrac{5}{3}x$$

B.

a)

$$slope=\dfrac{7-3}{4-0}=1$$

b)

$$slope=\dfrac{-2-6}{-1-(-9)}=-1$$

C.

a)

$$y-10=-2x$$

$$y=-2x+10$$

b)

$$y-(-2)=-3(x-4)$$

$$y=-3x+10$$

c)

$$y=4$$

$$y=-2x+10$$

d)

$$slope=\dfrac{1-(-2)}{-12-3}=-\dfrac{1}{5}$$

$$y-(-2)=-\dfrac{1}{5}(x-3)$$

$$y=-\dfrac{1}{5}x-\dfrac{7}{5}$$

e)

$$slope=\dfrac{450-240}{15-20}=-42$$

$$y-240=-42(x-20)$$

$$y=-42x+1080$$