Question

a line with a slope of -1 passes through the points (10, -7) and (u, -6). what is the value of u?
$u = \square$

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: Substitute known values

Let $(x_1,y_1)=(10,-7)$, $(x_2,y_2)=(u,-6)$, and $m=-1$.
$$-1=\frac{-6-(-7)}{u-10}$$

Step3: Simplify numerator

Calculate $-6-(-7)=-6+7=1$.
$$-1=\frac{1}{u-10}$$

Step4: Solve for $u$

Cross-multiply: $-1\times(u-10)=1$, so $-u+10=1$.
Rearrange: $-u=1-10=-9$, so $u=9$.

Answer:

$u=9$