Question

what are the coordinates of the midpoint of the line segment with endpoints j (-6, 3) and k (4, -2)? (-1, .5) (2,1) (-10,1) (-2,5) question 2 1 pts what is the slope of a line that is parallel to -x + 4y = 6? (convert the fraction into a decimal with 2 decimal places.)

Explanation:

Step1: Recall mid - point formula

The mid - point formula for two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$. Here, $x_1=-6,y_1 = 3,x_2 = 4,y_2=-2$.

Step2: Calculate x - coordinate of mid - point

$x=\frac{-6 + 4}{2}=\frac{-2}{2}=-1$.

Step3: Calculate y - coordinate of mid - point

$y=\frac{3+( - 2)}{2}=\frac{3 - 2}{2}=\frac{1}{2}=0.5$.

Step1: Rewrite the line equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope. Given $-x + 4y=6$, solve for $y$. Add $x$ to both sides: $4y=x + 6$. Then divide by 4: $y=\frac{1}{4}x+\frac{6}{4}=\frac{1}{4}x + 1.5$.

Step2: Determine the slope of the parallel line

Parallel lines have the same slope. The slope of the line $y=\frac{1}{4}x + 1.5$ is $\frac{1}{4}$. Converting $\frac{1}{4}$ to a decimal gives $m = 0.25$.

Answer:

(-1, 0.5)