Find the value of r so the line that passes through each pair of points has the given slope:

(12,10), (-2,r), m=-4

using the slope formula ... (r - 10) / (-2 - 12) = -4

solve for r

(r-10)/(-1-12) = -4

r-10 = 56
r = 66

To find the value of r, we can use the slope formula and substitute the coordinates of the points and the given slope.

The slope formula is given by:

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

Substituting the coordinates (12, 10) and (-2, r), we have:

-4 = (r - 10) / (-2 - 12)

Simplifying the equation, we get:

-4 = (r - 10) / (-14)

Cross multiply to eliminate the fraction:

-4 * (-14) = r - 10

56 = r - 10

To solve for r, add 10 to both sides of the equation:

56 + 10 = r

r = 66

Therefore, the value of r is 66.

To find the value of r so that the line passing through the given pair of points has the given slope, we can use the slope formula:

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

Given the points (12, 10) and (-2, r), and the slope m = -4, we can plug in these values into the slope formula and solve for r.

-4 = (r - 10) / (-2 - 12)

Now we can solve for r by cross-multiplying:

-4 * (-2 - 12) = r - 10

Simplifying:

-4 * (-14) = r - 10
56 = r - 10

Adding 10 to both sides:

56 + 10 = r
r = 66

Therefore, the value of r that makes the line passing through the points (12, 10) and (-2, r) have a slope of -4 is r = 66.