Answer
The equation of the required line in slope-intercept form is
y = (-2x/3) + (7/3)
Comparing this with y = mx + c,
Slope = m = (-2/3)
Intercept = c = (7/3)
Explanation
The slope and y-intercept form of the equation of a straight line is given as
y = mx + c
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
c = y-intercept of the line.
So, to solve this, we have to solve for the slope and then write the eqution in the slope-point form which we can then simplify to the slope-intercept form
The general form of the equation in point-slope form is
y - y₁ = m (x - x₁)
where
y = y-coordinate of a point on the line.
y₁ = This refers to the y-coordinate of a given point on the line
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
x₁ = x-coordinate of the given point on the line
The point is given as (x₁, y₁) = (-4, 5)
Then, we can calculate the slope from the information given
Two lines with slopes (m₁ and m₂) that are perpendicular to each other are related through
m₁ × m₂ = -1
From the line given,
y = (3/2)x - 2
We can tell that m₁ = (3/2), so, we can solve for m₂
(3/2) (m₂) = -1
m₂ = (2/3) (-1) = (-2/3)
We can then write the equation of the given line in slope-intercept form
y - y₁ = m (x - x₁)
y - 5 = (-2/3) (x - (-4))
y - 5 = (-2/3) (x + 4)
y - 5 = (-2x/3) - (8/3)
y = (-2x/3) - (8/3) + 5
y = (-2x/3) + (7/3)
Hope this Helps!!!
![\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~ -1 &,& -1~) \end{array} \\\\\\ % slope = m slope = m\implies 3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-1)=3[x-(-1)] \\\\\\ y+1=3(x+1)](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26%26%28~%20-1%20%26%2C%26%20-1~%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%20m%5Cimplies%203%0A%5C%5C%5C%5C%5C%5C%0A%25%20point-slope%20intercept%0A%5Cstackrel%7B%5Ctextit%7Bpoint-slope%20form%7D%7D%7By-%20y_1%3D%20m%28x-%20x_1%29%7D%5Cimplies%20y-%28-1%29%3D3%5Bx-%28-1%29%5D%0A%5C%5C%5C%5C%5C%5C%0Ay%2B1%3D3%28x%2B1%29)
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