The image contains the following problem:

"A line passes through point $(-2, 6)$ and has a slope of $-4$.
Write an equation in the form $y = mx + b$ for this line."

Solution:

We are asked to find the equation of a line, given:

• A point: $(-2, 6)$
• A slope: $m = -4$

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

We can substitute the values of the point $(-2, 6)$ and the slope $m = -4$ into the equation to find $b$.

Substituting: $6 = (-4)(-2) + b$ $6 = 8 + b$ $b = 6 - 8 = -2$

Thus, the equation of the line is: $y = -4x - 2$

Would you like more details, or do you have any questions about this solution?

Here are 5 related questions to expand your understanding:

1. How can we find the equation of a line if two points are given instead of a point and a slope?
2. What is the meaning of the slope in the context of a graph?
3. How can we convert a slope-intercept form to standard form $Ax + By = C$?
4. How can we find the x- and y-intercepts from the equation $y = -4x - 2$?
5. How would the equation change if the slope was positive?

Tip: Always substitute carefully when solving for the y-intercept to avoid sign errors!