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]
