Question: Topic 2 Test Review
1. What is the equation of the line shown in point-slope form?
A. y - 1 = 2(x + 2)
B. y - 1 = -2(x + 2)
C. y + 1 = -2(x - 2)
D. y + 1 = 2(x - 2)
y - y1 = m(x - x1)
2. Write the equation in slope-intercept form of a line parallel to y = -6x + 5 that passes through (-1, 4).
y = x +
3. Select ALL equations perpendicular to 4x + 12y = 9
y = 3x - 8
x = 4
Graph shape: a line with negative slope, descending from the upper-left to the lower-right, crossing the y-axis below the origin and crossing the x-axis to the left of the origin; position_hint: top-right
User: explain number 1 step by step
1. **State the problem:** We need to find the equation of the line in point-slope form from the given options.
2. **Recall the point-slope form formula:**
$$y - y_1 = m(x - x_1)$$
where $m$ is the slope and $(x_1, y_1)$ is a point on the line.
3. **Identify the point and slope from the options:**
- The point is given as $(-2, 1)$ or $(2, -1)$ depending on the sign inside the parentheses.
- The slope $m$ is either $2$ or $-2$.
4. **Analyze each option:**
- Option A: $y - 1 = 2(x + 2)$ means point $(-2, 1)$ and slope $2$.
- Option B: $y - 1 = -2(x + 2)$ means point $(-2, 1)$ and slope $-2$.
- Option C: $y + 1 = -2(x - 2)$ means point $(2, -1)$ and slope $-2$.
- Option D: $y + 1 = 2(x - 2)$ means point $(2, -1)$ and slope $2$.
5. **Use the graph description:** The line has a negative slope (descending from upper-left to lower-right), so slope $m$ must be negative.
6. **Choose the correct point:** The line crosses the y-axis below the origin and the x-axis to the left of the origin, consistent with point $(-2, 1)$.
7. **Conclusion:** The correct equation is option B:
$$y - 1 = -2(x + 2)$$