Complete the point-slope equation of the line through (-1,6) and (1,5). Use exact numbers. y-6=

Calculate the slope: To find the point-slope form of the equation of the line, we first need to calculate the slope of the line using the two given points (-1,6) and (1,5). The slope (m) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]Substitute coordinates into slope formula: Substitute the coordinates of the points into the slope formula: \[ m = \frac{5 - 6}{1 - (-1)} \] \[ m = \frac{-1}{2} \] The slope of the line is -1/2.Find the slope of the line: Now that we have the slope, we can use the point-slope form of the equation of a line, which is: \[ y - y_1 = m(x - x_1) \] We can use either of the two points for $ (x_1, y_1) $. Let's use the point (-1,6).Use the point-slope form: Substitute the slope and the coordinates of the point into the point-slope form: \[ y - 6 = -\frac{1}{2}(x - (-1)) \] \[ y - 6 = -\frac{1}{2}(x + 1) \] This is the point-slope equation of the line through the points (-1,6) and (1,5).

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

(-1,6)

and

(1,5)

\newline

Use exact numbers.

\newline

y-6=

Calculate the slope: To find the point-slope form of the equation of the line, we first need to calculate the slope of the line using the two given points ( $-1$ , $6$ ) and ( $1$ , $5$ ). The slope (m) is given by the formula: $\newline$ $m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute coordinates into slope formula: Substitute the coordinates of the points into the slope formula: $\newline$ $m = \frac{5 - 6}{1 - (-1)}$ $\newline$ $m = \frac{-1}{2}$ $\newline$ The slope of the line is $-1$ / $2$ .
Find the slope of the line: Now that we have the slope, we can use the point-slope form of the equation of a line, which is: $\newline$ $y - y_1 = m(x - x_1)$ $\newline$ We can use either of the two points for $(x_1, y_1)$ . Let's use the point ( $-1$ , $6$ ).
Use the point-slope form: Substitute the slope and the coordinates of the point into the point-slope form: $\newline$ $y - 6 = -\frac{1}{2}(x - (-1))$ $\newline$ $y - 6 = -\frac{1}{2}(x + 1)$ $\newline$ This is the point-slope equation of the line through the points ( $-1$ , $6$ ) and ( $1$ , $5$ ).