write the equation of the given parent graph with the points, (5,-2) and (6,0)
To find the equation of the parent graph given the points (5, -2) and (6, 0), we need to determine the values of the slope and y-intercept.
Using the slope formula:
slope (m) = (change in y) / (change in x)
Let's calculate the slope using the given points:
m = (0 - (-2)) / (6 - 5)
m = 2 / 1
m = 2
So, the slope of the parent graph is 2.
Now, we can use the point-slope form of a linear equation, which is: y - y1 = m(x - x1), where (x1, y1) represents a point on the line.
Using the point (5, -2), we substitute x1 = 5 and y1 = -2 into the equation:
y - (-2) = 2(x - 5)
y + 2 = 2(x - 5)
Next, we can simplify and rewrite the equation in slope-intercept form (y = mx + b) by expanding and rearranging:
y + 2 = 2x - 10
y = 2x - 10 - 2
y = 2x - 12
Therefore, the equation of the given parent graph passing through the points (5, -2) and (6, 0) is y = 2x - 12.
To find the equation of a parent graph passing through the given points (5, -2) and (6, 0), we need to determine the slope and y-intercept.
Step 1: Find the slope (m):
Use the formula for slope (m) given two points (x₁, y₁) and (x₂, y₂):
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points, (5, -2) and (6, 0), we can substitute the values into the formula:
m = (0 - (-2)) / (6 - 5)
= 2 / 1
= 2
So, the slope (m) is 2.
Step 2: Find the y-intercept (b):
We can use the slope-intercept form of the equation, y = mx + b, where m is the slope and b is the y-intercept.
Now we have the slope (m) as 2, and one of the points (6, 0). We can substitute these values into the equation:
0 = 2(6) + b
0 = 12 + b
To find the value of b, we rearrange the equation and isolate b:
b = -12
So, the y-intercept (b) is -12.
Step 3: Write the equation:
Now that we have m and b, we can write the equation of the parent graph. Substituting the values into the slope-intercept form, we have:
y = 2x - 12
Therefore, the equation of the parent graph passing through the points (5, -2) and (6, 0) is y = 2x - 12.
To write the equation of the parent graph, we need to determine the type of function that represents the graph. Since you haven't specified the type of function, we will assume that it is a linear equation.
A linear equation can be written in the form y = mx + b, where m represents the slope of the line, and b represents the y-intercept. To find the equation of the line, we need to find the values of the slope (m) and the y-intercept (b).
To find the slope (m), we use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Given the points (5, -2) and (6, 0), we can substitute the values into the formula:
m = (0 - (-2)) / (6 - 5)
m = 2 / 1
m = 2
Now that we have the slope (m = 2), we can find the y-intercept (b) by substituting the values of the slope and one of the points into the equation:
y = mx + b
-2 = 2(5) + b
-2 = 10 + b
b = -12
Therefore, the equation of the line representing the parent graph is:
y = 2x - 12