Answer
The equation of the line in point-slope form is
y - 5 = (-3/5) (x + 3)
We can simplify this to obtain the slope-intercept form
y - 5 = (-3/5) (x + 3)
y - 5 = (-3x/5) - (9/5)
y = (-3x/5) - (9/5) + 5
y = (-3x/5) + (16/5)
Then, to put the whole thing in a simplified equation form, we multiply through by 5
y = (-3x/5) + (16/5)
5y = -3x + 16
3x + 5y = 16
Explanation
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
So, we just need to compute the slope of this line since a point on the line has already been provided (-3, 5)
For two lines with slopes m₁ and m₂ that are perpendicular to each other, the slopes are related through the relation
m₁m₂ = -1
And the slope-intercept form of the equation of a straight line is given as
y = mx + b
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.
b = y-intercept of the line.
So, the slope of the line whose equation is given in the question is
m₁ = (5/3)
This is obtained by comparing y = mx + b with y = (5/3)x + 2
So, we can obtain the slope of the line that we need
m₁m₂ = -1
m₁ = (5/3)
m₂ = ?
m₁m₂ = -1
(5/3) × m₂ = -1
(5m₂/3) = -1
Cross multiply
m₂ = (-3/5)
So, we can write the equation in point-slope form now
Recall that
y - y₁ = m (x - x₁)
m = slope = (-3/5)
Point = (x₁, y₁) = (-3, 5)
x₁ = -3
y₁ = 5
y - y₁ = m (x - x₁)
y - 5 = (-3/5) (x - (-3))
y - 5 = (-3/5) (x + 3)
Hope this Helps!!!
