A straight line passes through the points $(3, -2)$ and $(4, 5)$ and intersects the y-axis at $-23$. We are asked to find the equation of the line.

1. Problem Description

A straight line passes through the points $(3, -2)$ and $(4, 5)$ and intersects the y-axis at $-23$. We are asked to find the equation of the line.

2. Solution Steps

We are given two points $(3, -2)$ and $(4, 5)$. We can find the slope $m$ of the line using the formula:

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

Using the given points, $(x_1, y_1) = (3, -2)$ and $(x_2, y_2) = (4, 5)$, we have:

$m = \frac{5 - (-2)}{4 - 3} = \frac{7}{1} = 7$

Since the line intersects the y-axis at $-23$, this means the y-intercept $b$ is $-23$. The equation of a line in slope-intercept form is given by:

$y = mx + b$

Substituting the values of $m$ and $b$, we get:

$y = 7x - 23$

3. Final Answer

The equation of the line is $y = 7x - 23$.