Question

The line on the graph passes through the points A (0, 6) and B (3, 0).

Answer 1

The equation for the line passing through point A and perpendicular to AB will be y-0.5x=6, the gradient of line AB is -2, and the gradient of a line perpendicular to AB is 0.5.

What is the slope or gradient?

A numerical assessment of a line's angle relative to the ground is known as the slope.

Given data;

m₁ is the slope of line AB

m₂ is the slope of a line perpendicular to AB

The coordinate points are,

A,(x₁,y₁)= (0, 6)

B,(x₂,y₂)=(3, 0).

The gradient of line AB;

$\rm m_{{1} }= \frac{y_2-y_1}{x_2-x_1} \\\\ \rm m_{{1} }= \frac{0-6}{3-0} \\\\ m_{{1} }=-2$

The slope of the lines has a perpendicular relation is -1;

m₁ × m₂ = -1

(-2) × m₂ = -1

m₂ = 1/2

m₂ = 0.5

The equation of the line passing through point A and perpendicular to AB;

(y - y₁) = m₂(x-x₁)

(y-6)=0.5(x-0)

y-6 = 0.5 x

y-0.5x=6

Hence, the gradient of line AB, the gradient of a line perpendicular to AB, and the equation of the line passing through point A and perpendicular to AB will be -2,0.5 and y-0.5x=6.

To learn more about the slope, refer to the link;

brainly.com/question/3605446

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