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complete the equation of the line through $(1,4)$ and $(2,2)$

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Cube roots of positive perfect cubes

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Q. complete the equation of the line through

(1,4)

and

(2,2)

Calculate Slope: To find the equation of a line, we need to determine the slope $m$ of the line using 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 the line passes through. $\newline$ Using the points $(1,4)$ and $(2,2)$ , we calculate the slope as follows: $\newline$ $m = \frac{2 - 4}{2 - 1}$ $\newline$ $m = \frac{-2}{1}$ $\newline$ $m = -2$
Use Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. $\newline$ Using the slope $m = -2$ and point $(1,4)$ , we plug these values into the point-slope form: $\newline$ $y - 4 = -2(x - 1)$
Simplify Equation: Next, we simplify the equation by distributing the slope $-2$ through the parentheses: $\newline$ $y - 4 = -2x + 2$
Convert to Slope-Intercept Form: To write the equation in slope-intercept form $y = mx + b$ , we add $4$ to both sides of the equation to solve for $y$ : $y = -2x + 2 + 4$ $y = -2x + 6$

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