Devon wants to write an equation for a line that passes through 2 of the data points he has collected. The points are (8, 5) and

The points given are (8,5) and (-12,-9). Calculating slope: slope = (-9 minus 5) divided by (-12 minus 8) equals -14 over -20, simplifying to 7 over 10. The line equation format is y = mx + b, with slope m = 7/10. Using point (8,5), substitute x = 8 and y = 5 to solve for b: 5 = 7/10 times 8 plus b; 5 = 56/10 plus b; subtracting 56/10 from both sides gives 5 minus 56/10 equals b; converting 5 to 50/10 minus 56/10 equals b; so b equals -3/5. Thus, the equation is y = (7/10)x - 3/5. Converting to standard form: multiply both sides by 10 gives 10y = 7x - 6; subtract 7x to get -7x + 10y = -6; multiply both sides by -1 results in 7x - 10y = 6. Therefore, the equation 7x - 10y = 3 is incorrect because the points do not satisfy it.

Answer:

Step-by-step explanation: Given points (8,5) and (-12,-9), calculate slope as (-9 - 5) divided by (-12 - 8), which is -14/-20, simplifying to 7/10. The line equation y = mx + b uses slope m = 7/10. Utilizing point (8,5), set x = 8 and y = 5 and solve for b: 5 = (7/10)*8 + b; thus 5 = 56/10 + b; subtracting 56/10 from both sides gives 5 - 56/10 = b; converting 5 into 50/10 yields 50/10 - 56/10 = b; so b = -3/5. The resulting equation is y = (7/10)x - 3/5. To write in standard form, multiply both sides by 10: 10y = 7x - 6; then subtract 7x: -7x + 10y = -6; multiplying both sides by -1 yields 7x - 10y = 6. Hence, the equation 7x - 10y = 3 is not a good fit because these points do not satisfy it.