Questions: Find an equation of the given line. (7/9, 8) and (-7/9, 7) on line Which equation below is the point-slope form of an equation of a line? A. y-x₁=m(x-y₁) B. y-y₁=m(x-x₁) C. Ax+By=C D. y=mx+b Find the slope of the line using the two given points. Recall that the slope is the change in y divided by the change in x. m=9/14 (Type an integer or a simplified fraction.) Now substitute the values for y₁, m, and x₁ into the point-slope equation. First substitute the values used in the equation, use the first ordered pair, (7/9, 8), in your calculations. y-□=m(x-x₁)

Solution Steps

To find the equation of the line given two points, we need to follow these steps:

1. Calculate the slope (m) using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
2. Use the point-slope form of the equation \( y - y_1 = m(x - x_1) \) with one of the given points.

Given the points \(\left(\frac{7}{9}, 8\right)\) and \(\left(-\frac{7}{9}, 7\right)\), we calculate the slope \(m\) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given values: \[ m = \frac{7 - 8}{-\frac{7}{9} - \frac{7}{9}} = \frac{-1}{-\frac{14}{9}} = \frac{-1 \times 9}{-14} = \frac{9}{14} \approx 0.6429 \]

The point-slope form of the equation of a line is: \[ y - y_1 = m(x - x_1) \] Using the first point \(\left(\frac{7}{9}, 8\right)\) and the calculated slope \(m = 0.6429\): \[ y - 8 = 0.6429 \left(x - \frac{7}{9}\right) \]

Among the given options, the correct point-slope form is: \[ y - y_1 = m(x - x_1) \] Thus, the answer is B.

Final Answer