write a linear equation relating x and y for each table
x (0,3,6,10)
y (20, 8,-4,-20)
starting with (0,20) note that as x grows by 3, y changes by -12
so the slope is -4
That means you have
y = -4x + b
Now use any point to find b.
To write a linear equation relating x and y using the given table, we can use the formula for the equation of a straight line, which is:
y = mx + b
Where:
- 'y' is the dependent variable (in this case, the values of y)
- 'x' is the independent variable (in this case, the values of x)
- 'm' is the slope of the line
- 'b' is the y-intercept (the value of y when x = 0)
To find the values of 'm' and 'b' for the linear equation, we can use the values from the table.
Step 1: Calculate the slope (m)
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the first two points (0, 20) and (3, 8), we can substitute these coordinates into the formula:
m = (8 - 20) / (3 - 0)
m = -12 / 3
m = -4
Step 2: Calculate the y-intercept (b)
The y-intercept (b) is the value of y when x = 0. Since we have the point (0, 20), we can directly obtain the value of b as 20.
Step 3: Write the linear equation
Now that we have the values of m and b, we can substitute them into the equation y = mx + b:
y = -4x + 20
Therefore, the linear equation relating x and y for the given table is y = -4x + 20.