Question

Create a circle with center A and a radius of your choice. Create a point B on the circle, and find the coordinates of B. Draw the radius . What is the slope-intercept form of the equation of ? Show your work.

Answer 1

Corrected Question

Create a circle with center A and a radius of your choice. Create a point B on the circle, and find the coordinates of B. Draw the radius AB. What is the slope-intercept form (y = mx + b) of the equation of AB? Show your work.

Answer:

y=0.62x+2

Explanation:

In the attached circle drawn using Geogebra

• Center is at point A(0,2)
• Point B on the circumference has coordinates (1.7,3.05)
• Radius of the circle=2 Units

Gradient of AB,
`m=(y_2-y_1)/(x_2-x_1)` where
`(x_1,y_1)=A(0,2)$ and (x_2,y_2)=B(1.7,3.05)`

`m=(3.05-2)/(1.7-0) \\=(1.05)/(1.7)\\\\\approx 0.62`

Line AB intercepts the y-axis at y=2, therefore: b=2

The slope-intercept form of the line AB (in this case) is therefore:

y=0.62x+2

For every circle center A of radius r and point B chosen on the circumference, the equation of the line AB will be different.

You can try one of your own!!