12. Reason The graphs of 4x + 12y = 8 andy = mx + 5 are perpendicular. What is thevalue of m?

Answer:   [tex]m=3[/tex] Step-by-step explanation: The equation of the line in Slope-Intercept form is: [tex]y=mx+b[/tex] Where "m" is the slope of the line and "b" is the y-intercept. Then, given the following equation: [tex]4x + 12y = 8[/tex] You can solve for "y" in order to write this equation in Slope-Intercept form: [tex]4x + 12y = 8\\\\12y=-4x+8\\\\y=-\frac{1}{3}x+\frac{2}{3}[/tex] As you can notice, the slope of this line (which we can call [tex]m_1[/tex]) is: [tex]m_1=-\frac{1}{3}[/tex] By definition, the slopes of perpendicular lines are negative reciprocals. Therefore, knowing this, you can determine that the slope fo the graph of [tex]y = mx + 5[/tex] is:   [tex]m=3[/tex]