To solve this problem, we need to find the equation of a line with a slope of $-3$ that passes through the point $(0, 7)$.

Solution:

1. The equation of a line in slope-intercept form is: $y = mx + b$ where $m$ is the slope and $b$ is the y-intercept.

2. Given:

   • Slope ($m$) = $-3$
   • The line passes through the point $(0, 7)$.

3. Since the line passes through $(0, 7)$, the y-intercept $b$ is $7$. This is because when $x = 0$, $y = b$.

4. Substitute $m = -3$ and $b = 7$ into the equation: $y = -3x + 7$

Answer:

The correct equation of the line is: $y = -3x + 7$

Correct Answer Choice:

The second option, $y = -3x + 7$, is the correct answer.

Do you have any questions or would you like a further breakdown?

Related Questions:

1. How do you find the equation of a line if given two points?
2. What is the significance of the slope in a line equation?
3. How do you convert a line equation from point-slope form to slope-intercept form?
4. How do you determine if two lines are parallel?
5. What is the formula for finding the midpoint between two points?

Tip:

Remember, the y-intercept $b$ in a line's equation $y = mx + b$ is simply the $y$-value when $x = 0$. This makes it easy to find when you have the slope and a point where $x$ is zero!