Question

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

Answer 1

Answer:

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

Option A is correct option.

Step-by-step 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:

$y-y_1=m(x-x_1)\\y-(-5)=-\frac{2}{3}(x-4)\\y+5=-\frac{2}{3}(x-4)$

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

Option A is correct option.