Questions: 2) Write an equation in slope-intercept form of the line that passes through (7, -10) with a slope of 0. A) y=-10 B) x=7 C) y=7 D) x=-10 Find the center and radius of (x+7)^2+(y+4)^2=36. A) (4,7), r=36 B) (-7,-4), r=6 C) (7,4), r=36 D) (-4,-7), r=

2) Write an equation in slope-intercept form of the line that passes through (7, -10) with a slope of 0. A) y=-10 B) x=7 C) y=7 D) x=-10 Find the center and radius of (x+7)^2+(y+4)^2=36. A) (4,7), r=36 B) (-7,-4), r=6 C) (7,4), r=36 D) (-4,-7), r=
Transcript text: 2) (1 pt) Write an equation in slope-intercept form of the line that passes through (7, -10 ) with a slope of 0 . A) $y=-10$ B) $x=7$ C) $y=7$ D) $x=-10$ (1 pt) Find the center and radius of $(x+7)^{2}+(y+4)^{2}=36$. A) $(4,7), r=36$ B) $(-7,-4), r=6$ C) $(7,4), r=36$ D) $(-4,-7), \mathrm{r}=$
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Solution

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Solution Steps

To solve the first question, we need to write the equation of a line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Given the slope is 0, the line is horizontal, and the y-value remains constant at the y-coordinate of the given point. For the second question, the equation of a circle is given in the form \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. We can identify the center and radius directly from the equation.

Step 1: Equation of the Line

Given the point \((7, -10)\) and a slope of \(0\), the equation of the line in slope-intercept form is given by: \[ y = mx + b \] Since the slope \(m = 0\), the equation simplifies to: \[ y = -10 \]

Step 2: Center and Radius of the Circle

The equation of the circle is given as \((x + 7)^2 + (y + 4)^2 = 36\). From this equation, we can identify the center \((h, k)\) and the radius \(r\):

  • The center is \((-7, -4)\).
  • The radius is calculated as \(r = \sqrt{36} = 6\).

Final Answer

The answers to the questions are:

  1. The equation of the line is \(\boxed{y = -10}\).
  2. The center of the circle is \(\boxed{(-7, -4)}\) and the radius is \(\boxed{6}\).
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