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Question 2 of 5

Identify the slope and [tex]\(y\)[/tex]-intercept of the function [tex]\(y = -2x + 1\)[/tex].

A. The slope is -2. The [tex]\(y\)[/tex]-intercept is [tex]\((0,1)\)[/tex].

B. The slope is 1. The [tex]\(y\)[/tex]-intercept is [tex]\((0,-2)\)[/tex].

C. The slope is 1. The [tex]\(y\)[/tex]-intercept is [tex]\((0,2)\)[/tex].

D. The slope is 2. The [tex]\(y\)[/tex]-intercept is [tex]\((0,1)\)[/tex].



Answer :

GinnyAnswer
Let's analyze the equation of the function given: [tex]\( y = -2x + 1 \)[/tex].

In the slope-intercept form of a linear equation, which is [tex]\( y = mx + b \)[/tex], the slope [tex]\( m \)[/tex] is the coefficient of [tex]\( x \)[/tex], and the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is the constant term.

1. Identify the slope:
- The equation is in the form [tex]\( y = mx + b \)[/tex].
- Here, the coefficient of [tex]\( x \)[/tex] is [tex]\(-2\)[/tex].
- Thus, the slope [tex]\( m \)[/tex] is [tex]\(-2\)[/tex].

2. Identify the [tex]\( y \)[/tex]-intercept:
- The [tex]\( y \)[/tex]-intercept is the constant term, the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex].
- In this equation, the constant term is [tex]\( 1 \)[/tex].
- Therefore, the [tex]\( y \)[/tex]-intercept is the point [tex]\((0, 1)\)[/tex].

Given these calculations:
- The slope is [tex]\(-2\)[/tex].
- The [tex]\( y \)[/tex]-intercept is [tex]\((0, 1)\)[/tex].

Now, let's match these values to the given choices:

A. The slope is -2. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 1) \)[/tex].

B. The slope is 1. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, -2) \)[/tex].

C. The slope is 1. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 2) \)[/tex].

D. The slope is 2. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 1) \)[/tex].

After comparing, we see that option A correctly identifies the slope and y-intercept.

Therefore, the correct answer is:
A. The slope is -2. The [tex]\( y \)[/tex]-intercept is [tex]\( (0, 1) \)[/tex].
kenneth7751

Answer:

Step-by-step explanation:

The given function is \( y = -2x + 1 \).

Let's identify the slope and the \( y \)-intercept:

1. **Slope:** The slope of a linear function in the form \( y = mx + b \) is represented by \( m \). In this case, \( m = -2 \).

2. **\( y \)-intercept:** The \( y \)-intercept is the point where the graph intersects the \( y \)-axis. It is represented as \( (0, b) \) in the equation \( y = mx + b \). Here, \( b = 1 \).

Therefore, according to the options provided:

A. The slope is \(-2\). The \( y \)-intercept is \((0,1)\).

This matches with the function \( y = -2x + 1 \).

So, the correct answer is \( \boxed{\text{A}} \).