Answer:
[tex]\bf Point \ slope \ form: y + 5 =\dfrac{-1}{2}(x -8)\\\\\\Slope-intercept \ form: y =\dfrac{-1}{2}x-1[/tex]
Step-by-step explanation:
Given equation: y = 2x + 5
This is in slope-intercept form, y= mx +b
Where 'm' is the slope and b is the y-intercept.
m₁ = 2
The product of slope of two perpendicular line = -1
[tex]\boxed{\bf \ m_2 = \dfrac{-1}{m_1}}[/tex]
[tex]m_2 = \dfrac{-1}{2}[/tex]
The line passes through (8, -5) and its slope is (-1/2).
Equation of line in point slope form:
[tex]\boxed{\sf y- y_1 = m(x - x_1)}[/tex]
[tex]\sf y - (-5) = \dfrac{-1}{2} (x - 8)\\\\\\y + 5 = \dfrac{-1}{2}(x - 8)[/tex]
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Writing the equation of the line in slope-intercept form:
[tex]\sf y = \dfrac{-1}{2}x + b[/tex]
This line is passing through (8,-5). Substitute in the above equation and find the value of 'b'.
[tex]\sf ~~~~~~-5 = \dfrac{-1}{2}*8+b\\\\\\~~~~~~~-5= -4+b\\\\\\~~-5+4 =b\\\\~~~~~~~~~~b = -1[/tex]
Equation of line in slope intercept form:
[tex]\bf y = \dfrac{-1}{2}x -1[/tex]
