Indicate the equation of the given line in standard form.

Question

The line with slope 9/7 and containing the midpoint of the segment whose endpoints are (2, -3) and (-6, 5).

Answer 1

Given that Midpoints are (2 , -3) and (-6 , 5) and

First you have to find the midpoint using formula

Here (x1 , y1) = (2 , -3) and (y1 , y2) = (-6 , 5)

= (-2 , 1)

Standard form of an equation of a line is y = mx + c

y = mx + c

Substitute the value of c in standard equation of line

y = mx + c

Answer 2

The standard form line equation is Ax + By = C. A shouldn't be negative, A and B shouldn't both be zero, and A, B and C should be integers.

Slope-intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

Let the end points are (x₁, y₁) = (2, - 3) and (x₂, y₂) = (- 6, 5).

Slope (m) = 9/7.

Now, the line equation is y = (9/7)x + b.

Mid point of the segment joining by the end points : [ (x₁ + x₂)/2, (y₁ + y₂)/2 ] = [ (2 - 6)/2, (- 3 + 5)/2 ] = [ - 4/2, 2/2 ] = [- 2, 1].

Find the y - intercept by substituting the mid point in the line equation say (x, y) = (- 2, 1).

1 = (9/7)(- 2) + b

b = 1 + (18/7)

⇒ b = 25/7.

The line equation in slope - intercept - form is y = (9/7)x + (25/7).

7y = 9x + 25

9x - 7y = - 25.

Therefore, the line equation in standard form is 9x - 7y = - 25 .