To solve this, we need to find the equation of a line passing through the point (2, ‒3) and parallel to the line given by $y = -4x - 5$.

Step 1: Identify the slope of the parallel line.

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. From the equation $y = -4x - 5$, the slope is $m = -4$.

Since Hilda's line is parallel to this line, it will have the same slope, so the slope of Hilda's line is also $m = -4$.

Step 2: Use the point-slope form to find the equation.

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

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

Where $(x_1, y_1)$ is a point on the line, and $m$ is the slope. Substituting the point $(2, -3)$ and the slope $m = -4$:

$y - (-3) = -4(x - 2)$ $y + 3 = -4(x - 2)$ $y + 3 = -4x + 8$ $y = -4x + 8 - 3$ $y = -4x + 5$

Step 3: Check the options.

The correct equation is $y = -4x + 5$.

Answer:

The correct equation is $y = -4x + 5$.

Would you like any further details or have any questions?

Related Questions:

1. How do you determine the slope of a parallel line?
2. How can you convert from point-slope form to slope-intercept form?
3. What is the difference between parallel and perpendicular lines in terms of slopes?
4. How would you find the equation of a line perpendicular to $y = -4x - 5$?
5. How do you verify that a point lies on a given line equation?

Tip:

Parallel lines always have the same slope, so use this property to quickly identify the slope of the new line.