## Questions and Answers

What is the equation of the line passing through the points (1, -1) and (3, 5)?

3x - y + 4 = 0

Define the y-intercept of a line.

The y-intercept is the point where the line intersects the y-axis, with coordinates (0, c).

What is the slope-intercept form of a line?

The slope-intercept form is y = mx + c, where m is the slope and c is the y-intercept.

How is the equation of a line found using the two-point form?

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What are the coordinates of the y-intercept of a line?

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Explain the concept of finding the equation of a line with slope and points.

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Find the equation of the line equidistant from the parallel lines $9x + 6y - 7 = 0$ and $3x + 2y + 6 = 0$.

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A ray of light passing through the point (1, 2) reflects on the x-axis at point A and passes through (5, 3). Find the coordinates of point A.

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Prove that the product of the lengths of the perpendiculars drawn from the point $\left(\frac{1}{\cos\theta}, \frac{1}{\sin\theta}\right)$ to the line $x\cos\theta + y\sin\theta = 1$ is $b^2$.

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A person wants to reach the path $6x - 7y + 8 = 0$ in the least time from the junction of paths $2x - 3y + 4 = 0$ and $3x + 4y - 5 = 0$. Find the equation of the path to follow.

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Explain the formula for the slope $m$ of a non-vertical line passing through points $(x_1, y_1)$ and $(x_2, y_2)$.

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What is the condition for two lines to be parallel? Provide the relationship involving their slopes.

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State the condition for a point to lie on a horizontal line.

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What is the equation of a horizontal line if it is at a distance a from the x-axis?

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Explain how to determine if a given point lies on a given line algebraically.

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If a line is horizontal and a distance a from the x-axis, what is the relationship between the points on the line and the ordinate value?

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What is the significance of the equation y = a or y = -a for a horizontal line?

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How does the equation y = a or y = -a help determine the position of a point on a horizontal line?

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