Question

Write the slope-intercept form of the equation of the line described. 8.) through: ( -4 , 5 ) , perpendicular to Y= 3/2x - 2

Answer 1

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!!!