Final answer:
To find the equation of a line using given x and y values, calculate the slope using the formula (y2 - y1) / (x2 - x1) and substitute it along with one set of coordinates into the equation y = mx + b. Given the points (-6, -3, 0, 3, 6) and (-6, -4, -2, 0, 2), we can choose two points (-6, -2) and (6, 2) to calculate the slope (1/3) and solve for the y-intercept (0), resulting in the equation y = (1/3)x.
Step-by-step explanation:
The equation of a line can be determined using the given information. In this case, we are given the values of x and y, which represents the coordinates of points on the line. To find the equation, we need to find the slope of the line (m) using the formula (y2 - y1) / (x2 - x1). Once we have the slope, we can substitute it along with one set of coordinates into the equation y = mx + b and solve for the y-intercept (b).
Given the points (-6, -3, 0, 3, 6) and (-6, -4, -2, 0, 2), we can choose any two points to calculate the slope. Let's use (-6, -2) and (6, 2). The slope (m) is (2 - (-2)) / (6 - (-6)) = 4 / 12 = 1/3. Now we can substitute the slope and one set of coordinates (let's use (-6, -2)) into the equation y = mx + b to solve for b. -2 = (1/3)(-6) + b. Simplifying this equation, we get b = -2 + 2 = 0. Therefore, the equation of the line is y = (1/3)x.