Complete the point-slope equation of the line through (-5,4) and (1,6). 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 (m) of the line using the two given points (-5,4) and (1,6). The slope 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: \[ m = \frac{6 - 4}{1 - (-5)} \] \[ m = \frac{2}{6} \] \[ m = \frac{1}{3} \] The slope of the line is $ \frac{1}{3} $.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 (1,6) into the point-slope form: \[ y - 6 = \frac{1}{3}(x - 1) \] This is the point-slope equation of the line through the points (-5,4) and (1,6).

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

(-5,4)

and

(1,6)

\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 (m) of the line using the two given points ( $-5$ , $4$ ) and ( $1$ , $6$ ). The slope 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: $\newline$ $m = \frac{6 - 4}{1 - (-5)}$ $\newline$ $m = \frac{2}{6}$ $\newline$ $m = \frac{1}{3}$ $\newline$ The slope of the line is $\frac{1}{3}$ .
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 ( $1$ , $6$ ) into the point-slope form: $\newline$ $y - 6 = \frac{1}{3}(x - 1)$ $\newline$ This is the point-slope equation of the line through the points ( $-5$ , $4$ ) and ( $1$ , $6$ ).