The required equation is 4x - 5y = 5

Given:

The Coordinates of the position P and Q are (5,3) and (10,7) respectively

To find:

What will be the equation of the line

Solution:

Equation of the line:

Equation of the line with points (x₁, y₁) and (x₂, y₂) is given by

            (y - y₁) = m (x - x₁)  

where slope (m) = (y₂ - y₁) /(x₂ -x₁)  

Here we have, P(5,3) and Q(10,7)  

Take P (5,3) = (x₁, y₁) and Q (10,7) = (x₂, y₂)

=>  slope (m) = (7 - 3) /(10 -5) = 4/5  

The equation of the line is

=>  (y - 3) = 4/5 (x - 5)  

=>  5y - 15 = 4x -20

=>  4x - 5y = 5

Therefore,

The required equation is 4x - 5y = 5

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Answer:

The required equation is 4x - 5y = 5

Step by Step:

A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane can aid in determining whether the line is parallel, perpendicular, or not.

Any two clearly separated points on a line can be used to calculate the slope of any line. Between two distinct points on a line, the slope of a line formula determines the ratio of "vertical change" to "horizontal change."

The Coordinates of the position P and Q are (5,3) and (10,7) respectively

Solution:

Equation of the line:

Equation of the line with points (x₁, y₁) and (x₂, y₂) is given by

           (y - y₁) = m (x - x₁)  

where slope (m) = (y₂ - y₁) /(x₂ -x₁)  

Here we have, P(5,3) and Q(10,7)  

Take P (5,3) = (x₁, y₁) and Q (10,7) = (x₂, y₂)

=>  slope (m) = (7 - 3) /(10 -5) = 4/5  

The equation of the line is

=>  (y - 3) = 4/5 (x - 5)  

=>  5y - 15 = 4x -20

=>  4x - 5y = 5

Therefore,

The required equation is 4x - 5y = 5

For more details on Slope of the Line, https://brainly.in/question/28301617

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