Question

Please help and show work!! I really need help please!!

Answer 1

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\-------------------------\\\\\text{We have}\ 5x+3y=8\qquad\text{subtract 5x from both sides}\\\\3y=-5x+8\qquad\text{divide both sides by 3}\\\\y=-\dfrac{5}{3}x+\dfrac{8}{3}\to m_1=-\dfrac{5}{3}\\\\\text{Therefore}\ m_2=-\dfrac{1}{-\frac{5}{3}}=\dfrac{3}{5}\\\\Answer:\ \boxed{b.\ \dfrac{3}{5}}$

--------------------------------------------------------

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{We have}\ 3x-5y=10\qquad\text{subtract 3x from both sides}\\\\-5y=-3x+10\qquad\text{divide both sides by (-5)}\\\\y=\dfrac{3}{5}x-2\to m_1=\dfrac{3}{5}\\\\\text{Therefore we have}\ m_2=\dfrac{3}{5}.\\\\Answer:\ \boxed{D.\ y=\dfrac{3}{5}x}$

Answer 2

Answer:

Answer Left Panel: 3/5 or B

Answer Right Panel: D

Step-by-step explanation:

Left Panel

• 5x + 3y = 8                         Subtract 5x from both sides
• 5x - 5x + 3y = - 5x + 8       Combine
• 3y = - 5x+ 8                       Divide by 3
• 3y/3 = -5x/3 + 8/3  
• y = - 5x/3  + 8/3                 The slope of any line is the number with the x
• Slope of this line = -5/3
• The slope of two lines that are perpendicular when multiplied = - 1
• slope of the given line(m1) * slope of the perpendicular(m2) = - 1
• m1 * m2 = - 1
• -5/3 * m2 = - 1                     Multiply by 3
• -5x/3 *3 = - 1 * 3                    
• -5x = - 3                               Divide by -5
• -5x/-5 = -3 / 5
• x = 3/5

Right Panel

The slope of a line parallel to another line is the same as the given line.

• The given line is 3x - 5y = 10            Subtract 3x from both sides
• 3x - 3x - 5y = -3x + 10                        Combine
• -5y = -3x + 10                                      Divide by - 5
• -5y/-5 = -3x/-5 + 10/-5                        Do the division
• y = 3x/5 - 2                                         So look for a line with a slope of 3/5
• y= 3x /5                                              Answer D