In a standard coordinate plane, what is the y-intercept of a line that passes through the points (3,17) and (5, 29)?

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In a standard coordinate plane, what is the y-intercept of a line that passes through the points (3,17) and (5, 29)?

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Answer 1 · 2018-04-21T08:23:59

$y-intercept = - 1$ $"y-intercept "=-1$

Explanation:

$the equation of a line in slope-intercept form$ $"the equation of a line in "color(blue)"slope-intercept form"$ is.

$∙ x y = m x + b$ $•color(white)(x)y=mx+b$

$where m is the slope and b the y-intercept$ $"where m is the slope and b the y-intercept"$

$to calculate m use the gradient formula$ $"to calculate m use the "color(blue)"gradient formula"$

$∙ x m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $•color(white)(x)m=(y_2-y_1)/(x_2-x_1)$

$let (x_{1}, y_{1}) = (3, 17) and (x_{2}, y_{2}) = (5, 29)$ $"let "(x_1,y_1)=(3,17)" and "(x_2,y_2)=(5,29)$

$\Rightarrow m = \frac{29 - 17}{5 - 3} = \frac{12}{2} = 6$ $rArrm=(29-17)/(5-3)=12/2=6$

$\Rightarrow y = 6 x + b \leftarrow is the partial equation$ $rArry=6x+blarrcolor(blue)"is the partial equation"$

$to find b substitute either of the 2 given points into$ $"to find b substitute either of the 2 given points into"$
$the partial equation$ $"the partial equation"$

$using (3, 17) then$ $"using "(3,17)" then"$

$17 = 18 + b \Rightarrow b = 17 - 18 = - 1$ $17=18+brArrb=17-18=-1$

$\Rightarrow y = 6 x - 1 \leftarrow in slope-intercept form$ $rArry=6x-1larrcolor(red)"in slope-intercept form"$

$\Rightarrow b = y-intercept = - 1$ $rArrb=" y-intercept "=-1$

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In a standard coordinate plane, what is the y-intercept of a line that passes through the points (3,17) and (5, 29)?

1 Answer

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