# Give the equation of the line perpendicular to the line described and satisfying the given conditions. y=-(4/3)x+5 with y-intercept (0, -8)

Question
Linear equations and graphs
Give the equation of the line perpendicular to the line described and satisfying the given conditions. $$\displaystyle{y}=-{\left(\frac{{4}}{{3}}\right)}{x}+{5}$$ with y-intercept (0, -8)

2021-02-04
Perpendicular lines have slopes that are negative reciprocals. Since the slope of the given line is $$\displaystyle-{\left(\frac{{4}}{{3}}\right)}$$ so the required slope is $$\displaystyle{m}=\frac{{3}}{{4}}$$. The y-intercept is (0,-8) so b=-8
Using slope-intercept form of a line, the equation is: y=mx+b
$$\displaystyle{y}=\frac{{3}}{{4}}{x}−{8}$$

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