Graph the equation (x-4)^2 + (y-2)^2 = 9
1 answer:
Answer: see graph below
<u>Step-by-step explanation:</u>
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center
- r is the radius
(x - 4)² + (y - 2)² = 9
- (h, k) = (4, 2)
- r² = 9 ⇒ r = 3
To graph the circle, mark an x at the center (4, 2). Then plot a point 3 units (the radius) to the right of the center, another point 3 units up from the center, a third point 3 units to the left of the center, and a fourth point 3 units down from the center. "Connect the dots" to form a circle.
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<h2>Linear Equations</h2>
Linear equations are often organized in slope-intercept form:
- <em>m</em> = slope
- <em>b</em> = y-intercept (the value of y when x=0)
Parallel lines always have the same slopes and different y-intercepts.
<h2>Solving the Question</h2>We're given:
- The line
- We must solve for a parallel line that passes through (0,2)
Firstly, rearrange the given line in slope-intercept form:
Remember, parallel lines always have the same slope. Therefore, our parallel line would look like this, with a (currently) unknown y-intercept (<em>b</em>):
We're given that the line passes through the point (0,2). Because the y-intercept occurs when x=0, we now know that the y-intercept of the line is 2. Plug this into the equation: