Final answer:
To find the value of a, we can use the formula for slope (m) of a line. Given the slope is -5 and two points, we can substitute these values into the formula and solve for a. Thus, the value of a is 5.
Step-by-step explanation:
To find the value of a, we can use the formula for slope (m) of a line:
m = (y2 - y1) / (x2 - x1)
Given that the slope is -5 and the two points are (2,3) and (a,-12), we can substitute these values into the formula:
-5 = (-12 - 3) / (a - 2)
Multiplying both sides of the equation by (a - 2), we get:
-5(a - 2) = -15
Simplifying the equation:
-5a + 10 = -15
Now, we can solve for a:
-5a = -25
a = 5
Therefore, the value of a is 5.