Answer:
Option (4). y = 3x - 5
Step-by-step explanation:
Given question is incomplete; here is the complete question.
What is the equation of the line that is perpendicular to the given line and passes through the point (3, 4)?
y = –1/3x + 5
y = –1/3x + 3
y = 3x + 2
y = 3x − 5
Line given in the graph passes through the points (-3, 2) and (0, 1).
Slope of the given line = [tex]\frac{y_{2}-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{2-1}{-3-0}[/tex]
m = [tex]-\frac{1}{3}[/tex]
Let the equation of a line perpendicular to this line is,
y - y' = m'(x - x') [Given line passes through (x', y')]
By the property of perpendicular lines,
m × m' = -1
([tex]-\frac{1}{3}[/tex]) × m' = -1
m' = 3
Equation of the perpendicular line will be,
y - 4 = 3(x - 3)
y - 4 = 3x - 9
y = 3x - 5
Option (4) will be the answer.
The equation of the line that is perpendicular to the given line is:
y = 3x – 5
The slope (also known as gradient) is defined as:
Slope (m) = change in y coordinate / change in x coordinate
m = (y₂ – y₁) / (x₂ – x₁)
m = (y₂ – y₁) / (x₂ – x₁)
m = (1 – 2) / (0 – –3)
m = –1/3
m₁ × m₂= –1
–1/3 × m₂ = –1
Cross multiply
–m₂ = –3
m₂ = 3
y – y₁ = m(x – x₁)
y – 4 = 3(x – 3)
Clear bracket
y – 4 = 3x – 9
Make y the subject by adding 4 to both side
y – 4 + 4 = 3x – 9 + 4
y = 3x – 5
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