Graph the line through the given point with the given slope.

(0, 2), m = - 5

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.

Graph the line through the given point with the given slope. (0, 2), m = -5

Learn how to graph the line that passes through point (0, 2) with a slope of -5 using the point-slope form of a linear equation. This step-by-step guide covers key algebraic concepts, including slopes and graphing techniques. Suitable for students in Grades 8-10.

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