The graph shows the altitude y , in meters, of a weather balloon x seconds after launch
(2,5), (4,20)
To find the equation of the graph, we need to determine the equation of the line that passes through the given points.
First, we'll find the slope of the line using the formula:
slope = (change in y) / (change in x)
slope = (20 - 5) / (4 - 2) = 15/2
Now, we'll use the slope-intercept form of the equation of a line, y = mx + b, where m is the slope and b is the y-intercept.
Using the point-slope form of the equation, we can substitute the values of one of the given points into the equation and solve for b.
Using the point (2,5):
5 = (15/2)(2) + b
5 = 15 + b
b = -10
So the equation of the graph is:
y = (15/2)x - 10
To find the equation of the graph given two points (2, 5) and (4, 20), we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope and b represents the y-intercept.
Step 1: Find the slope (m):
The slope can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (2, 5) and (4, 20):
m = (20 - 5) / (4 - 2)
m = 15 / 2
m = 7.5
Step 2: Find the y-intercept (b):
We can substitute one of the given points (2, 5) into the equation and solve for b.
5 = 7.5 * 2 + b
5 = 15 + b
b = 5 - 15
b = -10
Step 3: Write the equation:
Using the slope (m = 7.5) and the y-intercept (b = -10), the equation of the graph is:
y = 7.5x - 10
So, the altitude y, in meters, of the weather balloon x seconds after launch is given by the equation y = 7.5x - 10.
To find the equation for the altitude of the weather balloon, we can use the given points (2,5) and (4,20).
First, let's find the slope of the line passing through these two points using the formula:
slope = (change in y) / (change in x).
slope = (20 - 5) / (4 - 2) = 15 / 2 = 7.5.
Next, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1),
where (x1, y1) is the coordinate of any point on the line, and m is the slope.
Using the point (2,5), we have:
y - 5 = 7.5(x - 2).
Now we can simplify the equation:
y - 5 = 7.5x - 15,
y = 7.5x - 10.
Therefore, the equation for the altitude of the weather balloon is y = 7.5x - 10.