Pergunta

In the xy-plane, line l contains the points (2,6) and (8,10) Which of the following is an equation of line 1? A) y=(2)/(3)x+(14)/(3) B) y=(3)/(2)x-2 C) y=2x+6 D) y=8x+10
Solução

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MuriloMestre · Tutor por 5 anos
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To find the equation of line I, we can use the slope-intercept form of a linear equation: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.<br /><br />Step 1: Calculate the slope of line I using the given points $(2,6)$ and $(8,10)$.<br />The formula for the slope is: $m = \frac{y_2 - y_1}{x_2 - x_1}$<br /><br />Substituting the given points into the formula:<br />$m = \frac{10 - 6}{8 - 2} = \frac{4}{6} = \frac{2}{3}$<br /><br />Step 2: Use the slope-intercept form to find the equation of line I.<br />We know that the slope $m = \frac{2}{3}$ and we can use one of the given points to find the y-intercept $b$.<br /><br />Using the point $(2,6)$:<br />$6 = \frac{2}{3}(2) + b$<br />$6 = \frac{4}{3} + b$<br />$b = 6 - \frac{4}{3} = \frac{18}{3} - \frac{4}{3} = \frac{14}{3}$<br /><br />So, the equation of line I is:<br />$y = \frac{2}{3}x + \frac{14}{3}$<br /><br />Therefore, the correct answer is:<br />A) $y=\frac {2}{3}x+\frac {14}{3}$
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