Question

The points (-1,-2) and (11,r) lie on a line with slope (3)/(4). Find the missing coordinate r.

Answer 1

To find the missing coordinate r for a line with a slope of ⅓, we set up the equation based on the slope formula, (change in y) / (change in x), using the points (-1, -2) and (11, r). After cross-multiplying and simplifying the equation, we find that the missing coordinate r is 7.

Step-by-step explanation:

The student is asking how to find the missing coordinate r for the point (11, r) that lies on a line with a slope of ⅓.

To find this coordinate, we can use the formula for the slope of a line, which is (change in y) / (change in x) = slope. Here, we have the two points (-1, -2) and (11, r), and the slope is ¾.

First, we calculate the change in y, which is r - (-2) or r + 2, and the change in x, which is 11 - (-1) or 12. We can then set up the equation ¾ = (r + 2) / 12.

By cross-multiplying, we get 3×12 = 4(r + 2) which simplifies to 36 = 4r + 8. Subtracting 8 from both sides gives us 28 = 4r, and dividing by 4, we find that r = 7. Hence, the missing coordinate is 7.

Answer 2

To find the missing coordinate r, we can use the slope formula and the given points to set up an equation and solve for r. The missing coordinate is equal to 7.

Step-by-step explanation:

To find the missing coordinate r, we can use the slope formula which states that the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1)/(x2 - x1)

Using the given points (-1, -2) and (11, r), and the slope (3/4), we can set up the equation:

3/4 = (r - (-2))/(11 - (-1))

Simplifying the equation, we have:

3/4 = (r + 2)/12

Cross-multiplying, we get:

3(12) = 4(r + 2)

Solving for r, we have:

36 = 4r + 8

Subtracting 8 from both sides:

28 = 4r

Dividing by 4, we find that:

r = 7