how do i write an equation showing that mass as a function of volume for gold?
table shows
volume (cm^3)
1.0
2.0
3.0
4.0
5.0
mass(g)
19.4
38.6
58.1
77.4
96.5
Graph the data, the horizontal axis, volume, vertical axis mass.
It looks like a straight line
mass= k *volume + intercept
The intercept looks to be zero, so measure the slope on the graph.
how do i measure the slope?
thank you i understand now thank you for your time and knowledge :)
y=(19g/cm^3)V
To write an equation showing mass as a function of volume for gold, you need to determine the relationship between mass and volume based on the given data in the table. In this case, it appears that there is a linear relationship between mass and volume.
To find the equation, you can use the concept of slope and y-intercept from linear equations.
Step 1: Choose two points from the table. Let's take the points (1.0, 19.4) and (5.0, 96.5).
Step 2: Find the slope (m) using the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
m = (96.5 - 19.4) / (5.0 - 1.0)
m = 77.1 / 4.0
m = 19.275
Step 3: Substitute the values of one point and the slope into the point-slope form of a linear equation, y - y1 = m(x - x1). Let's use the point (1.0, 19.4).
y - 19.4 = 19.275(x - 1.0)
Step 4: Simplify the equation.
y - 19.4 = 19.275x - 19.275
y = 19.275x + 0.875
The equation y = 19.275x + 0.875 represents the relationship between mass (y) and volume (x) for gold, based on the given data.