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What are the slope and the [tex]\(y\)[/tex]-intercept of the linear function represented by the equation [tex]\(y = -10x + 1\)[/tex]?

A. The slope is [tex]\(-10\)[/tex], and the [tex]\(y\)[/tex]-intercept is [tex]\(-1\)[/tex].
B. The slope is [tex]\(-10\)[/tex], and the [tex]\(y\)[/tex]-intercept is [tex]\(1\)[/tex].
C. The slope is [tex]\(-1\)[/tex], and the [tex]\(y\)[/tex]-intercept is [tex]\(-10\)[/tex].
D. The slope is [tex]\(1\)[/tex], and the [tex]\(y\)[/tex]-intercept is [tex]\(-10\)[/tex].

Sagot :

GinnyAnswer
To determine the slope and the [tex]\( y \)[/tex]-intercept of a linear function given by the equation [tex]\( y = -10x + 1 \)[/tex], follow these steps:

1. Identify the form of the equation: The given equation [tex]\( y = -10x + 1 \)[/tex] is in the slope-intercept form. The standard form for a linear equation is [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.

2. Extract the slope [tex]\( m \)[/tex]: In the equation [tex]\( y = -10x + 1 \)[/tex], the coefficient of [tex]\( x \)[/tex] is [tex]\( -10 \)[/tex]. Therefore, the slope [tex]\( m \)[/tex] is [tex]\( -10 \)[/tex].

3. Extract the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex]: The constant term in the equation is [tex]\( 1 \)[/tex]. Therefore, the [tex]\( y \)[/tex]-intercept [tex]\( b \)[/tex] is [tex]\( 1 \)[/tex].

Thus, the correct answer is that the slope is [tex]\(-10\)[/tex], and the [tex]\( y \)[/tex]-intercept is [tex]\( 1 \)[/tex].

So, the correct choice is:
- The slope is -10, and the [tex]\( y \)[/tex]-intercept is 1.
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