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What are the slope and [tex]\( y \)[/tex]-intercept of the graph of [tex]\( 7x + y = 8 \)[/tex]?

A) Slope [tex]\( = -7 \)[/tex], [tex]\( y \)[/tex]-intercept [tex]\( = 8 \)[/tex]

B) Slope [tex]\( = -8 \)[/tex], [tex]\( y \)[/tex]-intercept [tex]\( = 7 \)[/tex]

C) Slope [tex]\( = -7 \)[/tex], [tex]\( y \)[/tex]-intercept [tex]\( = -8 \)[/tex]

D) Slope [tex]\( = 7 \)[/tex], [tex]\( y \)[/tex]-intercept [tex]\( = 8 \)[/tex]

Sagot :

GinnyAnswer
To find the slope and y-intercept of the graph given by the equation [tex]\(7x + y = 8\)[/tex], we need to convert this equation into the slope-intercept form, which is [tex]\(y = mx + b\)[/tex]. In this form, [tex]\(m\)[/tex] represents the slope and [tex]\(b\)[/tex] represents the y-intercept. Here is the step-by-step procedure:

1. Start with the given equation:
[tex]\[ 7x + y = 8 \][/tex]

2. Isolate [tex]\(y\)[/tex] on one side of the equation:

Subtract [tex]\(7x\)[/tex] from both sides to get:
[tex]\[ y = -7x + 8 \][/tex]

3. Identify the slope and the y-intercept:

The equation is now in the form [tex]\(y = mx + b\)[/tex].

- The coefficient of [tex]\(x\)[/tex] (which is [tex]\(-7\)[/tex]) is the slope [tex]\(m\)[/tex].
- The constant term (which is [tex]\(8\)[/tex]) is the y-intercept [tex]\(b\)[/tex].

Hence, the slope is [tex]\(-7\)[/tex] and the y-intercept is [tex]\(8\)[/tex].

Therefore, the correct answer is:
A) Slope [tex]\(=-7\)[/tex], y-intercept [tex]\(=8\)[/tex]
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