Answer :

The Equation of line passing through (10,10) is 8x - 5y = 30.

what is Equation of line?

A line's equation is just one way to express all the points that make up the line. Any point on a line will satisfy the general version of the equation, which is of the type axe + by + c = 0. The slope of the line and a point on the line are the two necessary components for the equation of a line to be formed.

solution:

Equation of line passing through (10,10).

Perpendicular to the line with equation : 5x + 8y = - 9.

As we know that,

Slope of perpendicular line : ax + by + c is b/a.

Slope of line : 5x + 8y = - 9  is  8/5.

Slope = m = 8/5.

As we know that,

Concepts.

Slope point form : The equation of a line with slope m and passing through a point (x₁, y₁) is : (y - y₁) = m(x - x₁).

Using this concept in this question, we get.

⇒ (y - 10) = 8/5(x - 10).

⇒ 5(y - 10) = 8(x - 10).

⇒ 5y - 50 = 8x - 80.

⇒ 8x - 80 - 5y + 50 = 0.

⇒ 8x - 5y - 30 = 0.

⇒ 8x - 5y = 30.

Therefore, Equation of line is 8x - 5y = 30.

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