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)

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

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

$y=-42x+1080$