Complete the point-slope equation of the line through (2,3) and (7,4). Use exact numbers. y-4=

Find the slope: First, we need to find the slope of the line that passes through the points (2,3) and (7,4). 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.Plug in the coordinates: Now, let's plug in the coordinates of the points into the slope formula: m = (4 - 3) / (7 - 2) m = 1 / 5 So, the slope of the line is 1/5.Calculate the slope: Next, we use the point-slope form of the equation of a line, which is: y - y1 = m(x - x1) We can use either of the two points for (x1, y1). Let's use the point (7,4).Use the point-slope form: Substitute the slope (m) and the coordinates of the point (7,4) into the point-slope equation: y - 4 = (1/5)(x - 7) This is the point-slope equation of the line through the points (2,3) and (7,4).

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

(2,3)

and

(7,4)

\newline

Use exact numbers.

\newline

y-4=

Find the slope: First, we need to find the slope of the line that passes through the points $(2,3)$ and $(7,4)$ . The slope $(m)$ is given by the formula: $\newline$ $m = \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
Plug in the coordinates: Now, let's plug in the coordinates of the points into the slope formula: $\newline$ m = $(4 - 3) / (7 - 2)$ $\newline$ m = $1 / 5$ $\newline$ So, the slope of the line is $1/5$ .
Calculate the slope: Next, we 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 $(7,4)$ .
Use the point-slope form: Substitute the slope ( extit{m}) and the coordinates of the point extit{( $7$ , $4$ )} into the point-slope equation: $\newline$ $y - 4 = \left(\frac{1}{5}\right)(x - 7)$ $\newline$ This is the point-slope equation of the line through the points extit{( $2$ , $3$ )} and extit{( $7$ , $4$ )}.