The equation you've provided is in slope-intercept form, $y = mx + b$, where:

• $m$ is the slope of the line,
• $b$ is the y-intercept.

For the equation $y = -4x - 3$:

• The slope ($m$) is $-4$.
• The y-intercept ($b$) is $-3$.

Interpretation:

1. Slope: A slope of $-4$ means that for every unit increase in $x$, the value of $y$ decreases by 4 units. The line is descending from left to right.

2. Y-intercept: The y-intercept is the point where the line crosses the y-axis. Here, it crosses the y-axis at $-3$ (i.e., at the point $(0, -3)$).

Graphing the Line:

• Start at the y-intercept, $(0, -3)$.
• From this point, use the slope to determine the direction of the line. Since the slope is $-4$, move one unit to the right (positive direction on the x-axis) and 4 units down (negative direction on the y-axis).
• Connect these points to form the line.

Would you like more details or have any questions?

Relative Questions:

1. How do you find the x-intercept of the line $y = -4x - 3$?
2. What would happen to the line if the slope were changed to $4$ instead of $-4$?
3. How would the graph change if the y-intercept was $3$ instead of $-3$?
4. Can you determine the equation of a line parallel to $y = -4x - 3$ that passes through the point $(1, 2)$?
5. What are the coordinates of another point on the line, besides $(0, -3)$?

Tip:

When graphing a linear equation, always identify the slope and y-intercept first. This makes it easier to sketch the graph accurately.