Final answer:
To find the missing coordinate r for the line with slope 3/4 passing through (-13,2) and (r,8), we use the slope formula and solve for r, obtaining r = -5.
Step-by-step explanation:
To find the missing coordinate r for the point on a line with a slope of 3/4, we can use the formula for slope which is change in y divided by change in x. The two points given are (-13, 2) and (r, 8). The slope between these two points should be equal to the slope of the line.
Slope formula: (y2 - y1) / (x2 - x1) = slope. Plugging in our values we get (8 - 2) / (r - (-13)) = 3/4, which simplifies to 6 / (r + 13) = 3/4. Cross-multiplying, we get 4 * 6 = 3 * (r + 13), which simplifies to 24 = 3r + 39. Subtracting 39 from both sides, we have -15 = 3r, and dividing by 3, r = -5. Therefore, the missing coordinate for r is -5.