Problem

Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form $y=m x+b$. \[ (8,9) ; x+7 y=8 \]

Solution

Step 1 :Given the equation of the line is \(x + 7y = 8\). We can rewrite this in slope-intercept form to find its slope. The slope-intercept form of the line is \(y = -\frac{1}{7}x + \frac{8}{7}\).

Step 2 :A line parallel to a given line will have the same slope. So, the slope of the line we are looking for is the same as the slope of the given line, which is \(-\frac{1}{7}\).

Step 3 :Once we have the slope, we can use the point-slope form of the line, \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is the given point, to find the equation of the line. Substituting the given point \((8,9)\) and the slope \(-\frac{1}{7}\) into the equation, we get \(y - 9 = -\frac{1}{7}(x - 8)\).

Step 4 :Finally, we can rewrite this equation in slope-intercept form to get the final answer. The equation of the line is \(y = -\frac{1}{7}x + \frac{71}{7}\).

From Solvely APP
Source: https://solvelyapp.com/problems/15925/

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