Answer :
Answer
Equation of the line is
7y = 4x + 30
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, to write the equation of the line, we need the slope of the line and a point on the line.
We already have (3, 6) as the point.
For the slope,
Two perpendicular lines with slopes m₁ and m₂ are related according to the relationship
m₁m₂ = -1
For the line whose equation is provided, we can find the slope of the line through
The slope and y-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, we will put the equation in this form to obtain the slope
7x = -4y + 6
4y = -7x + 6
Divide through by 4
(4y/4) = (-7x/4) + (6/4)
y = (-7/4) x + 1.5
Comaparing this with y = mx + b
m = Slope = (-7/4)
Back to the slope of the line we need
m₁m₂ = -1
m₁ = (-7/4)
(-7/4) × m₂ = -1
(-7m₂/4) = -1
Cross multiply
m₂ = (4/7)
So, recall,
y - y₁ = m (x - x₁)
m = slope = (4/7)
Point = (x₁, y₁) = (3, 6)
x₁ = 3
y₁ = 6
y - y₁ = m (x - x₁)
y - 6 = (4/7) (x - 3)
Multiply through by 7
7y - 42 = 4 (x - 3)
7y - 42 = 4x - 12
7y = 4x - 12 + 42
7y = 4x + 30
Hope this Helps!!!
