Answer:
the slope of the line that is perpendicular to the given line is [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
As the slope intercept form is
[tex]y=mx+b[/tex]
Where
- m is the slope
- b is the y-intercept
Considering the equation
[tex]5x+6y=42[/tex]
[tex]\mathrm{Slope-Intercept\:form\:of}\:5x+6y=42:\quad y=-\frac{5}{6}x+7[/tex]
[tex]\mathrm{Slope\:of\:}-\frac{5}{6}x+7:\quad m=-\frac{5}{6}[/tex]
As we know that perpendicular lines have negative reciprocal slopes.
So,
[tex]-\frac{1}{-\frac{5}{6}}=\frac{6}{5}[/tex]
Hence, the slope of the line that is perpendicular to the given line is [tex]\frac{6}{5}[/tex]
Keywords: slope, slope of a line, equation
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