The image presents several problems related to linear equations. I will solve question 1 and question 5. Question 1: Find the slope of a line that passes through the points $(-4, 6)$ and $(8, 2)$. Question 5: Write the equation for a line that has a slope of $-\frac{4}{5}$ and passes through $(-10, 6)$.

1. Problem Description

The image presents several problems related to linear equations. I will solve question 1 and question

5. Question 1: Find the slope of a line that passes through the points $(-4, 6)$ and $(8, 2)$.

Question 5: Write the equation for a line that has a slope of $-\frac{4}{5}$ and passes through $(-10, 6)$.

2. Solution Steps

Question 1:

To find the slope of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Here, $(x_1, y_1) = (-4, 6)$ and $(x_2, y_2) = (8, 2)$. Plugging these values into the formula, we get:

$m = \frac{2 - 6}{8 - (-4)} = \frac{-4}{8 + 4} = \frac{-4}{12} = -\frac{1}{3}$

Question 5:

To find the equation of a line with a given slope $m$ and passing through a point $(x_1, y_1)$, we can use the point-slope form of the equation of a line:

$y - y_1 = m(x - x_1)$

Here, $m = -\frac{4}{5}$ and $(x_1, y_1) = (-10, 6)$. Plugging these values into the point-slope form, we get:

$y - 6 = -\frac{4}{5}(x - (-10))$

$y - 6 = -\frac{4}{5}(x + 10)$

$y - 6 = -\frac{4}{5}x - \frac{4}{5}(10)$

$y - 6 = -\frac{4}{5}x - 8$

$y = -\frac{4}{5}x - 8 + 6$

$y = -\frac{4}{5}x - 2$

3. Final Answer

Question 1: The slope of the line is $-\frac{1}{3}$.

Question 5: The equation of the line is $y = -\frac{4}{5}x - 2$.