To graph the line that passes through the point $(0, 2)$ with a slope of $m = -5$, we can follow these steps:

Step 1: Use the point-slope form of the equation of a line.

The point-slope form is given by: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is the point on the line, and $m$ is the slope.

Here, $(x_1, y_1) = (0, 2)$ and $m = -5$. Substituting these values into the formula:

$y - 2 = -5(x - 0)$

Simplify:

$y - 2 = -5x$ $y = -5x + 2$

Step 2: Identify key points on the line.

• The y-intercept is $(0, 2)$ because when $x = 0$, $y = 2$.
• From the slope $m = -5$, this means that for every 1 unit increase in $x$, $y$ decreases by 5 units (since the slope is negative).

Step 3: Plot the graph.

You can now plot the points on the coordinate plane and draw the line:

1. Plot the point $(0, 2)$.
2. From this point, move 1 unit to the right (increase $x$ by 1) and 5 units down (decrease $y$ by 5) to plot another point at $(1, -3)$.
3. Draw a straight line through these points.

Would you like me to graph this equation for you? Let me know!

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Related Questions:

1. How do you find the slope from two given points?
2. What is the significance of the y-intercept in a line equation?
3. How can you rewrite the equation $y = -5x + 2$ in standard form?
4. What happens if the slope is positive instead of negative?
5. How do you find the equation of a line parallel to another line?

Tip: The slope of a line is a measure of its steepness and can be thought of as "rise over run" between two points.