Question

Identify an equation in point-slope form the line parallel to y=-2/3x+8 that passes through(4, -5).

A. y+5=-2/3(x-4)
B. y-5=-2/3(x+4)
C. y+5=3/2(x-4)
D. y-4=2/3(x+5)

Answer 1

The answer is A.

Explanation:

Answer 2

The equation of line in point slope form is:
`\mathbf{y+5=-(2)/(3) (x-4)}`

Option A is correct option.

Explanation:

We need to identify an equation in point-slope form the line parallel to y=-2/3x+8 that passes through(4, -5).

The general equation of point slope form is:
`y-y_1=m(x-x_1)`

where m is slope of the equation.

Finding slope of the equation.

Since the two lines are parallel so, both lines have same slope.

Equation of given line: y=-2/3x + 8

This equation is in slope-intercept form, comparing with general equation
`y=mx+b` where m is slope , we get the value of m= -2/3

So, slope of given line = m = -2/3

Slope of required line = m =-2/3

Now, writing equation in point-slope form:

We are given point (4,-5) so, we have
`x_1=4, y_1=-5` and slope is: m=-2/3

So, equation of line in point-slope form is:

`y-y_1=m(x-x_1)\\y-(-5)=-(2)/(3)(x-4)\\y+5=-(2)/(3)(x-4)`

So, the equation of line in point slope form is:
`\mathbf{y+5=-(2)/(3) (x-4)}`

Option A is correct option.