High School

What is the equation of a line with a slope of -5 and a [tex]y[/tex]-intercept of 7?

A. [tex]y=-\frac{5}{7} x[/tex]

B. [tex]y=7 x-5[/tex]

C. [tex]y=5 x-7[/tex]

D. [tex]y=-5 x+7[/tex]

Answer :

Certainly! Let's find the equation of the line given its slope and [tex]\( y \)[/tex]-intercept.

### Step-by-Step Solution

1. Identify the information given:
- The slope ([tex]\( m \)[/tex]) is [tex]\(-5\)[/tex].
- The [tex]\( y \)[/tex]-intercept ([tex]\( b \)[/tex]) is [tex]\( 7 \)[/tex].

2. Understand the form of the equation of a line:
- The equation of a line in slope-intercept form is written as:
[tex]\[
y = mx + b
\][/tex]
- Here, [tex]\( m \)[/tex] represents the slope, and [tex]\( b \)[/tex] represents the [tex]\( y \)[/tex]-intercept.

3. Substitute the given slope and [tex]\( y \)[/tex]-intercept into the slope-intercept form:
- Substitute [tex]\(-5\)[/tex] for [tex]\( m \)[/tex].
- Substitute [tex]\( 7 \)[/tex] for [tex]\( b \)[/tex].
[tex]\[
y = -5x + 7
\][/tex]

Therefore, the equation of the line with a slope of [tex]\(-5\)[/tex] and a [tex]\( y \)[/tex]-intercept of [tex]\( 7 \)[/tex] is:
[tex]\[
y = -5x + 7
\][/tex]

### Answer:
[tex]\[
y = -5x + 7
\][/tex]

So, the correct choice from the given options is:
[tex]\[
\boxed{y = -5x + 7}
\][/tex]

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