Given the linear equations (2x + 3y = 6) and (4x - ky = 12), for what value of (k) will the lines be parallel?

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Accepted Answer

Step:1 ：Step 1: Convert both equations into slope-intercept form ((y = mx + b)), where (m) represents the slope.Step:2 ：For the first equation, (2x + 3y = 6) becomes (y = -frac{2}{3}x + 2), so its slope is (-frac{2}{3}).Step:3 ：For the second equation, (4x - ky = 12) becomes (y = frac{4}{k}x - frac{12}{k}). Therefore, its slope is (frac{4}{k}).Step:4 ：Step 2: Since parallel lines have the same slope, we can set the slopes equal to each other and solve for (k).Step:5 ：(-frac{2}{3} = frac{4}{k}) implies that (k = -6).

Answer

Step: 1 ：Step 1: Convert both equations into slope-intercept form ((y = mx + b)), where (m) represents the slope.Step: 2 ：For the first equation, (2x + 3y = 6) becomes (y = -frac{2}{3}x + 2), so its slope is (-frac{2}{3}).Step: 3 ：For the second equation, (4x - ky = 12) becomes (y = frac{4}{k}x - frac{12}{k}). Therefore, its slope is (frac{4}{k}).Step: 4 ：Step 2: Since parallel lines have the same slope, we can set the slopes equal to each other and solve for (k).Step: 5 ：(-frac{2}{3} = frac{4}{k}) implies that (k = -6).

Given the linear equations \(2x + 3y = 6\) and \(4x - ky = 12\), for what value of \(k\) will the lines be parallel?

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