Which of the following is an equation for the line that passes through the point (0,0) and is perpendicular to the line shown above ?

Answer:Option A. [tex]y=\frac{5}{4}x[/tex]Step-by-step explanation:step 1Find the slope of the line shown in the graphThe given line pass through the points (0,3) and (5,-1) (see the graph)The formula to calculate the slope between two points is equal to[tex]m=\frac{y2-y1}{x2-x1}[/tex]substitute the values[tex]m=\frac{-1-3}{5-0}[/tex][tex]m=\frac{-4}{5}[/tex][tex]m=-\frac{4}{5}[/tex]step 2Find the slope of the line perpendicular to the line shown in the graphRemember thatIf two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)[tex]m_1*m_2=-1[/tex]we have[tex]m_1=-\frac{4}{5}[/tex]  ---> slope of the line shown in the graphsubstitute[tex](-\frac{4}{5})*m_2=-1[/tex]therefore[tex]m_2=\frac{5}{4}[/tex]step 3Find the equation of the line that passes through the point (0,0) and is perpendicular to the given line in the graphwe have[tex]m=\frac{5}{4}[/tex][tex]point\ (0,0)[/tex]Remember thatIf a line pass through the origin, then represent a proportional relationshipThe linear equation is equal to [tex]y=mx[/tex]substitute[tex]y=\frac{5}{4}x[/tex]