Question

the points (6, -3) and (5, t) fall on a line with a slope of -8. what is the value of t?
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Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$.

Step2: Plug in known values

Substitute $m=-8$, $(x_1,y_1)=(6,-3)$, $(x_2,y_2)=(5,t)$:
$$-8=\frac{t-(-3)}{5-6}$$

Step3: Simplify denominator

Calculate $5-6=-1$:
$$-8=\frac{t+3}{-1}$$

Step4: Solve for $t$

Multiply both sides by $-1$, then subtract 3:
$$8=t+3 \implies t=8-3$$

Answer:

$5$