Final answer:
To find the equation of the line that passes through the points (1/6, 0), (−7, 0), and (0, 7), we can first find the slope using the slope formula. Then, we can use the slope-intercept form of a linear equation to find the equation of the line.
Step-by-step explanation:
To find the equation of the line that passes through the points (1/6, 0), (−7, 0), and (0, 7), we need to find the slope of the line first. The slope can be found using the formula: slope (m) = (y2 - y1) / (x2 - x1). Let's choose the points (1/6, 0) and (0, 7) to find the slope:
m = (0 - 7) / (1/6 - 0) = -7 / (1/6) = -42
Now, we can use the slope-intercept form of a linear equation, which is y = mx + b. We know the slope (m = -42) and one point (0, 7), so we can substitute these values into the equation to find the y-intercept (b):
7 = -42(0) + b
b = 7
Therefore, the equation of the line is y = -42x + 7.