Final answer:
To find the equation of a line that passes through two points, we use the slope-intercept form of a linear equation. The equation of the line that passes through the points (6, -11) and (7, 2) is y = 13x - 89.
Step-by-step explanation:
To find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation, y = mx + b. First, we need to find the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1). Using the given points (6, -11) and (7, 2), we can plug in the values and solve for the slope. m = (2 - (-11)) / (7 - 6) = 13 / 1 = 13.
Next, we can choose either point to substitute into the equation. Let's use (6, -11). We have -11 = 13(6) + b. Solving for b, we get b = -11 - 78 = -89.
Therefore, the equation of the line that passes through the points (6, -11) and (7, 2) is y = 13x - 89.