Step 1: Write down the formula for the slope of a line. The slope $s$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $$ s = \frac{y_2 - y_1}{x_2 - x_1} $$ Step 2: Substitute the given values into the formula. Given points are $(m, -5)$ and $(1, 5)$. So, $x_1 = m$, $y_1 = -5$, $x_2 = 1$, $y_2 = 5$. The given slope is $s = \frac{1}{2}$. $$ \frac{1}{2} = \frac{5 - (-5)}{1 - m} $$ Step 3: Simplify the numerator. $$ \frac{1}{2} = \frac{5 + 5}{1 - m} $$ $$ \frac{1}{2} = \frac{10}{1 - m} $$ Step 4: Cross-multiply to solve for $m$. $$ 1 \times (1 - m) = 2 \times 10 $$ $$ 1 - m = 20 $$ Step 5: Isolate $m$. $$ -m = 20 - 1 $$ $$ -m = 19 $$ $$ m = -19 $$ The value of $m$ is $\boxed{-19}$. Step 1: Multiply the numerators and the denominators. $$ \frac{2}{5} \times \frac{18}{4} = \frac{2 \times 18}{5 \times 4} $$ $$ = \frac{36}{20} $$ Step 2: Simplify the fraction by dividing the numerator and the denominator by their greatest common divisor. The greatest common divisor of 36 and 20 is 4. $$ \frac{36 \div 4}{20 \div 4} = \frac{9}{5} $$ The simplified expression is $\boxed{\frac{9}{5}}$. Send me the next one 📸