Write Point-Slope Form Given Slope And A Point Worksheet

6 problems

To write the point-slope form of a line when given a slope and a point, use the formula  y - y_1 = m(x - x_1). Here, m represents the slope, and (x_1, y_1) is the point given. For example, if the slope ‘m’  is 2 and the point is (3, 4), you substitute these values into the formula: y - 4 = 2(x - 3). This equation shows how the line relates to the given point and slope, making it clear how the line moves through that specific point with the specified slope.

Algebra 1
Linear Relationship

How Will This Worksheet on "Write Point-Slope Form Given Slope and a Point" Benefit Your Student's Learning?

• Demonstrates how a point and slope define a straight line.
• Helps find the rate of change or predict situations based on initial conditions.
• Enhances algebra skills and orientation towards math tasks.
• Clearly shows number connections, making it easier to explain ideas.

How to Write Point-Slope Form Given Slope and a Point?

• Let the slope be $$m$$ and the point be $$(x_1, y_1)$$.
• The point-slope form is: $$y - y_1 = m(x - x_1)$$.
• Replace $$m$$ with the given slope.
• Replace $$x_1$$ and $$y_1$$ with the coordinates of the given point.
• Expand and simplify the equation to make it look cleaner if needed.

Solved Example

Q. A line with a slope of $9$ passes through the point $(9,9)$. What is its equation in point-slope form?
Solution:
1. Define Point-Slope Form: Point-slope form is $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is the point the line passes through.
2. Identify Slope and Point: We know the slope $m$ is $9$ and the point is $(9,9)$, so we plug these values into the point-slope form.
3. Substitute Values into Formula: $y - 9 = 9(x - 9)$ is the equation in point-slope form.

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