Final answer:
The missing coordinate r for the line with a slope of 3/2 and points (-6, r) and (2, 3) is -6, found by using the slope formula and algebraic manipulation.
Step-by-step explanation:
The student wants to find the missing coordinate r for the point (-6, r) that lies on the line with a known point (2, 3) and a slope of 3/2. We can use the formula for the slope m between two points (x1, y1) and (x2, y2) which is m = (y2 - y1) / (x2 - x1). Plugging in our values, the slope formula becomes 3/2 = (3 - r) / (2 - (-6)). After solving for r, we find that r = -6.
Step-by-step:
- Insert the known slope and points into the slope formula: (3 - r) / (2 - (-6)) = 3/2.
- Calculate the difference in x-coordinates: 2 - (-6) = 8.
- Multiply both sides of the equation by 8 to isolate the r variable: 3 - r = 12.
- Rearrange the equation to solve for r: r = 3 - 12.
- Finally, calculate the value of r: r = -6.