The center of a circle is at the origin on a coordinate grid. a line with a positive slope intersects the circle at (0, 7). which statement must be true?
a- the circle has a radius greater than 7.
b- the circle has a radius equal to 7.
c- the slope of the line is equal to 7.
d- the slope of the line is not equal to 7.

B statement is true.

Step-by-step explanation:

Given : A line with a positive slope intersects the circle at (0, 7).

To find : Which statement must be true.

Solution : we know that

The equation of the circle into center-radius form is ,

(x-h)²+(y-k)²= r²

where ,(h,k) is the center of the circle , r is the radius of the circle

In this problem

The center of the circle is the point (0,0)

The point (0,7) satisfies the equation of the circle

substitute the values in the equation

(0-0)² +(7-0)²=r²

(7)²=r²

r=7 units

The radius of the circle is 7 units

Therefore, B statement is true.

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.

the answer is d

hope this