<p>Find the number of integral values of <p>m</p> such that the line <p>3x + 4mx + 4 = 9</p> has specific intersection properties.</p>
Step-by-Step Solution
Key Concept: Determine the conditions for the parameter m by solving the intersection equation and identifying integral solutions.
<p><strong>Step 1:</strong> Rearranging the equation:</p><p>\[3x + 4mx + 4 = 9\]</p><p><strong>Step 2:</strong> Solving for the coefficient condition:</p><p>\[x = \frac{5}{3 + 4m}\]</p><p><strong>Step 3:</strong> For specific intersection properties, <p>3 + 4m = ±1, ±5</p>.</p><p><strong>Step 4:</strong> This gives:</p><p>\[m = -\frac{1}{2}, -1, \frac{1}{2}, -2\]</p><p><strong>Step 5:</strong> The integral values are <p>m = −1</p> and <p>m = −2</p>.</p><p>∴ Number of integral values = <strong>2</strong>.</p>
Correct Answer: 2