Question

You are tasked to graphing the equation
𝑦
=
−
5
𝑥

+

5
y=−5x + 5
Our initial point (the y-intercept) is the point is (
,
)



To plot a 2nd point we would start at our initial point and go down
−
5
−5 and right
1
1 and this is the point (
,
)



55

Answer 1

Let's break down the equation and find the points needed to graph \( y = -5x + 5 \).

### Step 1: Find the y-intercept
The y-intercept of a linear equation in the form \( y = mx + b \) occurs when \( x = 0 \).

Substituting \( x = 0 \) into the equation:

\[
y = -5(0) + 5 = 5
\]

So the y-intercept is the point \( (0, 5) \).

### Step 2: Plot a 2nd point
To plot a second point, we can use the slope of the line. The slope \( m \) in this equation is -5, which can be interpreted as:

- Go down 5 (since it's negative)
- Go right 1

Starting from the initial point \( (0, 5) \):

1. From \( (0, 5) \), go down 5 units:
\[
5 - 5 = 0 \quad \Rightarrow \quad y \text{ coordinate is now } 0
\]

2. Then, go right 1 unit from \( x = 0 \):
\[
0 + 1 = 1 \quad \Rightarrow \quad x \text{ coordinate is now } 1
\]

Thus, the second point is \( (1, 0) \).

### Summary of points:
- The initial point (y-intercept) is \( (0, 5) \).
- The second point calculated is \( (1, 0) \).

You can now plot these points to graph the line for the equation \( y = -5x + 5 \).