Step 1a

First, to find the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by: \$m = (y2 - y1) / (x2 - x1)\$

Explanation: To find the slope (m) of a line passing through two points (x1, y1) and (x2, y2), use this formula:

\$m = (y2 - y1) / (x2 - x1)\$

Step 2a

Let’s plug in the coordinates of the given points (1, -2) and (4, -5): \$m = (-5 - (-2)) / (4 - 1)\$ then \$m = (-5 + 2) / 3 \$ m = -1.

Explanation: To find the coordinates of the given points, (1, -2) and (4, -5), we can input them into the equation and determine that the slope is -1.

Step 3a

In this step, Use the point-slope form. Now that we have the slope (m = -1) and one point (1, -2), we can write the equation of the line: y − y1 = m(x − x1)

⇒y - (-2) = -1(x - 1)

⇒ y + 2 = -1 (x) + 1

⇒ y = -1 (x) + 1 - 2

⇒ y = -1 (x) - 1

Explanation: To proceed, apply the point-slope form. With the slope (m = -1) and one point (1, -2), we can formulate the equation of the line as follows: y − y1 = m(x − x1). Therefore, substituting the values, we get y - (-2) = -1(x - 1).

Step 4a

Let’s move on to the next step, where we will compare the equation with slope-intercept form (y = mx + b), where "b" represents the y-intercept.

Here’s the simplified equation is : y = -1 (x) - 1

After further simplification, we get: y = - 1(x) + (-1)

From the above equation we get y-intercept(b) = -1

Explanation: Convert the equation to slope - intercept form, y = mx + b, where "b" is the y - intercept. The simplified equation is y = - 1(x) + (-1).

Step 5a

So, the equation of the line passing through the points (1, -2) and (4, -5) is y = -x - 1.

Explanation: The equation for the line that passes through the coordinates (1, -2) and (4, -5) is y = -x - 1.