Hilda wrote an equation of a line that passes through the point (2,‒3) parallel to the line y = ‒4x – 5. Which equation represents Hilda’s equation?
Group of answer choices

y = ‒4x + 5

y = ‒4x + 9

x ‒ 4y = – 3

4x + y = 2

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.

Hilda wrote an equation of a line that passes through the point (2,‒3) parallel to the line y = ‒4x – 5. Which equation represents Hilda’s equation?

Learn how to find the equation of a line that passes through the point (2, -3) and is parallel to y = -4x - 5. This step-by-step guide covers the use of point-slope and slope-intercept forms to derive the equation. Suitable for students in Grades 8-10.

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