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

Step-by-step 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, $m=\dfrac{y_2-y_1}{x_2-x_1}$ where $(x_1,y_1)=A(0,2) and (x_2,y_2)=B(1.7,3.05)$

$m=\dfrac{3.05-2}{1.7-0} \\=\dfrac{1.05}{1.7}\\\\\approx 0.62$

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!!