write the equation of the given parent graph with the points, (5,-2), (6,0),
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To write the equation of the parent graph given the points (5,-2) and (6,0), we need to identify the type of parent graph that passes through these points.
Without more information or context, it is difficult to determine the specific parent graph. However, we can provide general steps to find the equation of linear parent graph passing through the given points.
Step 1: Identify the slope (m) of the linear parent graph.
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the given points (5, -2) and (6, 0):
m = (0 - (-2)) / (6 - 5)
m = 2 / 1
m = 2
Step 2: Use the point-slope form of a linear equation.
Using one of the given points (let's use (5, -2)), we can use point-slope form to write the equation:
y - y1 = m(x - x1)
y - (-2) = 2(x - 5)
y + 2 = 2(x - 5)
Step 3: Simplify and rewrite the equation in slope-intercept form.
Distribute 2 to the terms within the parentheses:
y + 2 = 2x - 10
Subtract 2 from both sides:
y = 2x - 12
Therefore, the equation of the linear parent graph passing through the points (5, -2) and (6, 0) is y = 2x - 12.
To write the equation of the parent graph with the given points, we need to determine the shape of the parent graph. The given points (5,-2) and (6,0) lie on the graph, but it is necessary to know the type of graph to proceed.
Without additional information about the parent graph, it is difficult to give a precise equation. However, I can explain how to approach this type of problem and provide some examples of parent graphs with their equations:
1. Linear Parent Graph:
- If the graph is a straight line and the points fall on that line, the equation will be in the form of y = mx + b, where m represents the slope of the line and b is the y-intercept.
- For example, if the points (5,-2) and (6,0) lie on a linear parent graph, we can find the equation using the slope formula:
- m = (change in y) / (change in x)
= (0 - (-2)) / (6 - 5)
= 2 / 1
= 2
- Now, let's substitute one of the points into the equation to find the y-intercept:
- Using (6,0): 0 = (2)(6) + b
- Solving for b, we get b = -12
- Therefore, the equation of the linear parent graph is y = 2x - 12.
2. Quadratic Parent Graph:
- If the graph is a parabola, the equation will be in the form of y = ax^2 + bx + c, where a, b, and c represent coefficients.
- To find the equation using the given points, you need to substitute them into the equation and solve the resulting system of equations.
- Unfortunately, without additional information, it is impossible to determine the equation of the quadratic parent graph with only two points. You would need at least three points to find a unique equation.
3. Other Parent Graphs:
- Depending on the type of parent graph, such as cubic, absolute value, square root, etc., the equation will have a specific format.
- Without knowing the type of parent graph or having more points, it is challenging to find the exact equation.
In summary, to find the equation of the parent graph using points, you need to determine the type of graph and its specific equation format. Then, substitute the given points into the equation and solve for any unknown coefficients.