Complete the point-slope equation of the line through (1,3) and (5,1). Use exact numbers. y-3=

Calculate Slope: To find the point-slope form of the line, we first need to calculate the slope of the line using the two given points (1,3) and (5,1). The slope (m) is given by the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Let's calculate the slope: m = (1 - 3) / (5 - 1) = -2 / 4 = -1/2Use Point-Slope Form: Now that we have the slope, we can use the point-slope form equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is one of the points the line passes through. We can use either point, but let's use the point (1,3). Let's plug in the values: y - 3 = (-1/2)(x - 1)Finalize Point-Slope Form: We have now found the point-slope form of the line using the slope we calculated and one of the given points. There is no need to simplify further as we are asked to use exact numbers.

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Q. Complete the point-slope equation of the line through

(1,3)

and

(5,1)

\newline

Use exact numbers.

\newline

y-3=

Calculate Slope: To find the point-slope form of the line, we first need to calculate the slope of the line using the two given points $(1,3)$ and $(5,1)$ . The slope $m$ is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points. $\newline$ Let's calculate the slope: $\newline$ $m = \frac{1 - 3}{5 - 1} = \frac{-2}{4} = -\frac{1}{2}$
Use Point-Slope Form: Now that we have the slope, we can use the point-slope form equation $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is one of the points the line passes through. We can use either point, but let's use the point $(1,3)$ . Let's plug in the values: $y - 3 = \left(-\frac{1}{2}\right)(x - 1)$
Finalize Point-Slope Form: We have now found the point-slope form of the line using the slope we calculated and one of the given points. There is no need to simplify further as we are asked to use exact numbers.