Answer:
Equation of line in slope-intercept form that passes through (4, -8) and is perpendicular to the graph [tex]y= \frac {2}{5} x - 3[/tex] is below
[tex]y = - \frac {5}{2} x + 2[/tex]
Step-by-step explanation:
Slope of the equation [tex]y= \frac{2}{5} x -3[/tex] is [tex]m_1 = \frac{2}{5}[/tex]
Since slopes of perpendicular lines are negative reciprocal of each other, therefore slope of other line is given as
[tex]m_2 = - \frac {1}{m_1} = - \frac {5}{2}[/tex]
Equation of line in point slope form is given as
[tex]y-y_1=m_2(x-x_1)[/tex]
Here (x1, y1) = (4, -8)
[tex]y+8 = - \frac{5}{2} (x-4)[/tex]
Simplifying it further
[tex]y = - \frac {5}{2} x + \frac {5}{2} 4 - 8[/tex]
[tex]y = - \frac {5}{2} x + 2[/tex]
