Solve for
a if the line through the two given points has the given slope.
(4,a) and (-2,-2a), m=-1
(Y2 - Y1) / (X2-X1) = -1
(-2a - a ) / (-2 -4) = -1
-3a = 6
a = -2
now put that back in and see if it works
To solve for the value of a, we need to find the equation of the line passing through the two given points and having a slope of -1.
The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the slope of the line is -1, we can substitute this value into the equation:
y = -x + b
To determine b, we need to use one of the given points on the line. Let's use the point (4,a). Plugging in these values into the equation, we get:
a = -(4) + b
Next, we can simplify the equation:
a = -4 + b
Now, let's use the other given point (-2,-2a) to find the value of a. Plugging in these values into the equation, we get:
-2a = -(-2) + b
Simplifying further:
-2a = 2 + b
To eliminate b, we can solve both equations simultaneously. Subtract the first equation from the second equation:
-2a - a = 2 + b - (-4 + b)
Simplifying further:
-3a = 6
Now, divide both sides of the equation by -3:
a = 6 / -3
Thus, the value of a is -2.