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 (–12, –9). He writes the equation
7x – 10y = 3. Is this a good model? Explain your reasoning.
To determine if the equation 7x - 10y = 3 is a good model for the line passing through the points (8, 5) and (-12, -9), we can substitute each point into the equation to see if they satisfy it.
For the point (8, 5):
7(8) - 10(5) = 56 - 50 = 6 ≠ 3
For the point (-12, -9):
7(-12) - 10(-9) = -84 + 90 = 6 ≠ 3
Since both points do not satisfy the equation 7x - 10y = 3, this equation is not a good model for the line passing through the given data points.