Question

Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) $$ \frac{\text { Point }}{(1,7)} \quad \frac{\text { Slope }}{m=-3} $$

Short answer

The three additional points on the given line are at (2,4), (0,10), and (-1,13).

Step-by-step solution

Find the Formula of the Line

Using the commonly used formula for a line in 2D space, \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-axis intercept, we can substitute the given point (1,7) and the slope \(m = -3\) to solve for \(b\). Plug in the values into the formula, we get \(7 = -3 * 1 + b\). Solving for \(b\), we find that \(b = 10\).

Calculate Additional Points

Using the line formula \(y = -3x + 10\), we can calculate new points by choosing different x-values, and calculate the corresponding y-values. \nFor example, for x = 2, we calculate y as \(y = -3*2 + 10 = 4\), getting point (2,4). \nWe apply the same procedure for two more x-values: x = 0 and x = -1 generating two more data points (0,10) and (-1,13).

Verify the Points on the Line

To ensure the calculated points indeed lie on the line, they can be validated by plugging them back into the equation of the line and checking if both sides of the equation are equal. For example, for x = 0, y = 10, substituting these values in the line equation, we get \(10 = -3*0 + 10\), which holds true