Complete the point-slope equation of the line through (1,0) and (6,-3). Use exact numbers. y-(-3)=

Find the slope: First, we need to find the slope of the line that passes through the points (1,0) and (6,-3). The slope (m) is given by the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]Calculate the slope: Now, let's plug in the coordinates of the two points into the slope formula: \[ m = \frac{-3 - 0}{6 - 1} \] \[ m = \frac{-3}{5} \] So, the slope of the line is $-\frac{3}{5}$.Use point-slope form: Next, we 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 (6, -3).Substitute values into equation: Substituting the slope and the coordinates of the point (6, -3) into the point-slope form, we get: \[ y - (-3) = -\frac{3}{5}(x - 6) \] This is the point-slope equation of the line through the points (1,0) and (6,-3).

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

(1,0)

and

(6,-3)

\newline

Use exact numbers.

\newline

y-(-3)=\square

Find the slope: First, we need to find the slope of the line that passes through the points ( $1$ , $0$ ) and ( $6$ , $-3$ ). The slope (m) is given by the formula: $\newline$ $m = \frac{y_2 - y_1}{x_2 - x_1}$
Calculate the slope: Now, let's plug in the coordinates of the two points into the slope formula: $\newline$ $m = \frac{-3 - 0}{6 - 1}$ $\newline$ $m = \frac{-3}{5}$ $\newline$ So, the slope of the line is $-\frac{3}{5}$ .
Use point-slope form: 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 ( $6$ , $-3$ ).
Substitute values into equation: Substituting the slope and the coordinates of the point ( $6$ , $-3$ ) into the point-slope form, we get: $\newline$ $y - (-3) = -\frac{3}{5}(x - 6)$ $\newline$ This is the point-slope equation of the line through the points ( $1$ , $0$ ) and ( $6$ , $-3$ ).