The problem asks us to find the slope of the given line and then find the equation of the line in standard form, using the graph of the line. Two points are given: $(-3, 2)$ and $(4, -1)$.

1. Problem Description

The problem asks us to find the slope of the given line and then find the equation of the line in standard form, using the graph of the line. Two points are given: $(-3, 2)$ and $(4, -1)$.

2. Solution Steps

a) Find the slope of the line.

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

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

Using the given points $(-3, 2)$ and $(4, -1)$, we have $x_1 = -3$, $y_1 = 2$, $x_2 = 4$, and $y_2 = -1$.

Substituting these values into the formula for the slope:

$m = \frac{-1 - 2}{4 - (-3)} = \frac{-3}{4 + 3} = \frac{-3}{7}$

b) Find the equation of the line in standard form.

The point-slope form of a line is given by:

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

Using the point $(-3, 2)$ and the slope $m = -\frac{3}{7}$, we have:

$y - 2 = -\frac{3}{7}(x - (-3))$

$y - 2 = -\frac{3}{7}(x + 3)$

Multiply both sides by 7 to eliminate the fraction:

$7(y - 2) = -3(x + 3)$

$7y - 14 = -3x - 9$

Rearrange the equation to get it in the standard form $Ax + By = C$:

$3x + 7y = 14 - 9$

$3x + 7y = 5$

3. Final Answer

a) The slope of the line is $-\frac{3}{7}$.

b) The equation of the line in standard form is $3x + 7y = 5$.