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Answer:
1.To rewrite the equation 2x - y = 4 in the form y = mx + b, we'll isolate y by adding y to both sides: 2x - y + y = 4 + y. This gives us 2x = 4 + y. Now, we'll subtract 4 from both sides: 2x - 4 = y. So the equation is y = 2x - 4. The slope (m) is 2 and the y-intercept (b) is -4.
2.To rewrite the equation 3x + 5y = 9 in the form y = mx + b, we'll isolate y by subtracting 3x from both sides: 3x + 5y - 3x = 9 - 3x. This gives us 5y = 9 - 3x. Now, we'll divide both sides by 5: y = (9 - 3x) / 5. So the equation is y = (9/5) - (3/5)x. The slope (m) is -3/5 and the y-intercept (b) is 9/5.
3.To rewrite the equation x/3 + y/5 = 1 in the form y = mx + b, we'll multiply both sides by 15: 5x + 3y = 15. Now, we'll isolate y by subtracting 5x from both sides: 5x + 3y - 5x = 15 - 5x. This gives us 3y = 15 - 5x. Now, we'll divide both sides by 3: y = (15 - 5x) / 3. So the equation is y = (15/3) - (5/3)x. The slope (m) is -5/3 and the y-intercept (b) is 15/3.
4.To rewrite the equation 6x + 5y + 14 = 0 in the form y = mx + b, we'll isolate y by subtracting 6x from both sides: 6x + 5y + 14 - 6x = 0 - 6x. This gives us 5y = -14 - 6x. Now, we'll divide both sides by 5: y = (-14 - 6x) / 5. So the equation is y = -2.8 - 1.2x. The slope (m) is -1.2 and the y-intercept (b) is -2.8.
5.To rewrite the equation y - 3 = 2(x - 5) in the form y = mx + b, we'll distribute the 2 on the right side: y - 3 = 2x - 10. Now, we'll isolate y by adding 3 to both sides: y - 3 + 3 = 2x - 10 + 3. This gives us y = 2x - 7. So the equation is y = 2x - 7. The slope (m) is 2 and the y-intercept (b) is -7.
6.To rewrite the equation y + 5 = - 2(x + 1) in the form y = mx + b, we'll distribute the -2 on the right side: y + 5 = -2x - 2. Now, we'll isolate y by subtracting 5 from both sides: y + 5 - 5 = -2x - 2 -
5. This gives us y = -2x - 7. So the equation is y = -2x - 7. The slope (m) is -2 and the y-intercept (b) is -7.
7.To rewrite the equation x - 3y = 6(y - 7x) + 10 in the form