Find the slope-intercept form for the line passing through ((1)/(7),(8)/(9)) and ((1)/(8),(7)/(8)).

Find Slope: Find the slope (m) of the line using the slope formula m = (y2 - y1) / (x2 - x1). We have two points (x1, y1) = (1/7, 8/9) and (x2, y2) = (1/8, 7/8). So, m = ((7/8) - (8/9)) / ((1/8) - (1/7)).Calculate Slope: Calculate the slope (m). m = ((7/8) - (8/9)) / ((1/8) - (1/7)) m = ((63/72) - (64/72)) / ((7/56) - (8/56)) m = (-1/72) / (-1/56) m = (1/72) * (56/1) m = 56/72 m = 7/9Find Y-Intercept: Use one of the points to find the y-intercept (b) using the point-slope form y - y1 = m(x - x1). Let's use the point (1/7, 8/9). 8/9 = (7/9)(1/7) + bSolve for b: Solve for b. 8/9 = (7/9)(1/7) + b 8/9 = 1/9 + b b = 8/9 - 1/9 b = 7/9Write Equation: Write the equation in slope-intercept form y = mx + b. Using the slope m = 7/9 and y-intercept b = 7/9, the equation is: y = (7/9)x + 7/9

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Find the slope-intercept form for the line passing through $\left(\frac{1}{7},\frac{8}{9}\right)$ and $\left(\frac{1}{8},\frac{7}{8}\right)$ .

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Algebra 1

Multiplication with rational exponents

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Q. Find the slope-intercept form for the line passing through

\left(\frac{1}{7},\frac{8}{9}\right)

and

\left(\frac{1}{8},\frac{7}{8}\right)

Find Slope: Find the slope $m$ of the line using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . We have two points $(x_1, y_1) = (\frac{1}{7}, \frac{8}{9})$ and $(x_2, y_2) = (\frac{1}{8}, \frac{7}{8})$ . So, $m = \frac{(\frac{7}{8}) - (\frac{8}{9})}{(\frac{1}{8}) - (\frac{1}{7})}$ .
Calculate Slope: Calculate the slope $m$ . $m = \frac{(\frac{7}{8}) - (\frac{8}{9})}{(\frac{1}{8}) - (\frac{1}{7})}$ $m = \frac{(\frac{63}{72}) - (\frac{64}{72})}{(\frac{7}{56}) - (\frac{8}{56})}$ $m = \frac{-\frac{1}{72}}{-\frac{1}{56}}$ $m = \frac{1}{72} \times \frac{56}{1}$ $m = \frac{56}{72}$ $m = \frac{7}{9}$
Find Y-Intercept: Use one of the points to find the y-intercept $b$ using the point-slope form $y - y_1 = m(x - x_1)$ . Let's use the point $(\frac{1}{7}, \frac{8}{9})$ . $\frac{8}{9} = \frac{7}{9}(\frac{1}{7}) + b$
Solve for b: Solve for b. $\newline$ $\frac{8}{9} = \left(\frac{7}{9}\right)\left(\frac{1}{7}\right) + b$ $\newline$ $\frac{8}{9} = \frac{1}{9} + b$ $\newline$ $b = \frac{8}{9} - \frac{1}{9}$ $\newline$ $b = \frac{7}{9}$
Write Equation: Write the equation in slope-intercept form $y = mx + b$ . Using the slope $m = \frac{7}{9}$ and y-intercept $b = \frac{7}{9}$ , the equation is: $y = \left(\frac{7}{9}\right)x + \frac{7}{9}$