Click and drag the labeled coordinate point to \( (-5,2) \) and use the m -slider to set a slope \( \mathrm{m}=7 \). Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed. Click here to launch the interactive figure. Which of the following points is on the line? A. \( (-4,6) \) B. \( (5,-4) \) C. \( (-6,-5) \) D. \( (-4,5) \)

To find which point is on the line with a slope of \( m = 7 \) and passing through \( (-5, 2) \), we use the point-slope form of a line: \[ y - y_1 = m(x - x_1) \] Substituting the coordinates and slope gives us: \[ y - 2 = 7(x + 5) \] Now, calculate for \( y \) when \( x \) is equal to each of the provided options to see which point satisfies the equation. Evaluating the points, we find that option A, \( (-4,6) \), satisfies the equation. Now, let's consider a related aspect. Each coordinate point represents a unique location on the Cartesian plane, and understanding how points relate to lines helps in visualizing mathematical concepts. The interplay of slopes and points is vital when graphing, making it easier to connect linear equations to real-world scenarios, like plotting a flight path or tracking a moving vehicle! Moreover, experimenting with different slopes and coordinates can be a great way to reinforce learning. Try swapping points or tweaking slopes; seeing how the line shifts can enhance your intuition about linear relationships. Don't forget to keep a journal of your findings for quick reference!