To find the linear equation for the given table of values, we can start by identifying the pattern between the \(x\) and \(y\) values.
We can calculate the slope (\(m\)) using the formula: \[ m = \frac{\Delta y}{\Delta x} \]
Let's take two points from the table, for example, \((32, 17)\) and \((35, 26)\): \[ m = \frac{26 - 17}{35 - 32} = \frac{9}{3} = 3 \]
Now, we have the slope \(m = 3\). Next, we can use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Using one of the points, say \((32, 17)\): \[ y - 17 = 3(x - 32) \]
Now, let's simplify this equation: \[ y - 17 = 3x - 96 \] \[ y = 3x - 79 \]
Thus, the equation that represents the relationship between \(x\) and \(y\) from the table is: \[ y = 3x - 79 \]
1 answer