Find the equation of the circle in the first image. Write it in standard form. Find the values of m and b in the second image. Find the x- and y- intercepts algebraically: -2x - 3y = -48
Find the equation of the circle in the first image. Write it in standard form. Find the values of m and b in the second image. Find the x- and y- intercepts algebraically: -2x - 3y = -48
Find the equation of the circle in the first image. Write it in standard form. Find the values of m and b in the second image. Find the x- and y- intercepts algebraically: -2x - 3y = -48
Find the equation of the circle in the first image. Write it in standard form.
Find the values of m and b in the second image.
Find the x- and y- intercepts algebraically: -2x - 3y = -48
Transcribed Image Text:### Understanding Linear Graphs
This graph represents a linear equation plotted on a two-dimensional plane, with both the x-axis (horizontal) and y-axis (vertical) extending from -10 to 10.
#### Key Features of the Graph:
1. **Axes and Grid**:
- The graph features both x (horizontal) and y (vertical) axes clearly labeled from -10 to 10.
- The grid lines create a reference framework for plotting points.
2. **Line Characteristics**:
- A red linear line is drawn from the third quadrant, starting approximately at the intersection of \( x = -8 \) and \( y = -10 \), passing through the origin (0, 0), and continuing upwards into the first quadrant, ending approximately at the intersection of \( x = 10 \) and \( y = 8 \).
- This line suggests a positive slope, meaning as values of \( x \) increase, the values of \( y \) also increase.
#### Analysis:
- The consistent upward movement of the line from left to right confirms it is a line with a positive slope.
- The line passes through the origin, indicating the equation of this line could be in the format of \( y = kx \), where \( k \) is the slope. Given the angle, it seems the line has a slope of 1, making the probable linear equation \( y = x \).
#### Educational Insight:
This type of graph is fundamental in understanding linear relationships in algebra and geometry. It showcases the direct proportional relationship, where for every unit increase in \( x \), \( y \) also increases proportionally by the same amount, illustrating the concept of a slope and its positive value.
Transcribed Image Text:This image features a graph of a circle plotted on a Cartesian coordinate system. The graph is designed with both horizontal and vertical grid lines, forming squares for ease of reference.
Here is a detailed description of the elements in the graph:
1. **Axes:**
- **X-Axis (Horizontal Axis):** Labeled with numbers ranging from -11 to 1. Each increment represents one unit.
- **Y-Axis (Vertical Axis):** Labeled with numbers ranging from -4 to 8. Each increment represents one unit.
2. **Circle:**
- **Equation:** The circle is centered at the point (-5, 2) in the Cartesian plane.
- **Radius:** The circle appears to extend 3 units in every direction from its center. Hence, the radius of the circle is 3 units.
- **Color:** The circle is outlined in blue.
The circle's exact placement and size in the graph can be described by the equation \( (x + 5)^2 + (y - 2)^2 = 9 \), where \((h, k)\) is the center of the circle \((-5, 2)\) and \(r\) is the radius (3 units).
Two-dimensional figure measured in terms of radius. It is formed by a set of points that are at a constant or fixed distance from a fixed point in the center of the plane. The parts of the circle are circumference, radius, diameter, chord, tangent, secant, arc of a circle, and segment in a circle.
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