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)
Step-by-step 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!!!