How do you write the equation of the line in slope intercept form passing through (1, 2) and (2, 5)?

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How do you write the equation of the line in slope intercept form passing through (1, 2) and (2, 5)?

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Answer 1 · 2018-04-20T10:23:39

y = 3x -1

Explanation:

Find the slope by using the formula $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/(x_2-x_1)$
You wil get: $\frac{5 - 2}{2 - 1}$ $(5-2)/(2-1)$
Simplify to get 3
Find the y-intercept by plugging in one kf the pairs and the slope into the y = mx + b equation. It doesn’t matter which pair you use.

You see 2 = 3(1) + b
Solve for b
2 = 3 + b
-1 = b

Answer is y = 3x -1

Answer 2 · 2018-04-20T10:24:54

$y = 3 x - 1$ $y=3x-1$

Explanation:

the gradient/slope is the difference in the $y$ $y$ values divided by the difference in the $x$ $x$ values.

$\Rightarrow$ $=>$ $\frac{5 - 2}{2 - 1}$ $[5-2]/[2-1]$ = $\frac{3}{1}$ $3/1$ =3

so the equation of the line is $y = 3 x + c$ $y=3x+c$

Use (1,2) $\Rightarrow$ $=>$ $2 = 3 \times 1 + c$ $2=3xx1+c$
$\Rightarrow$ $=>$ $2 = 3 + c$ $2=3+c$ so $c$ $c$ =-1

this gives $y = 3 x - 1$ $y=3x-1$

Answer 3 · 2018-04-20T10:25:14

$y = 3 x - 1$ $y=3x-1$

Explanation:

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

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

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

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

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

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

$\Rightarrow m = \frac{5 - 2}{2 - 1} = 3$ $rArrm=(5-2)/(2-1)=3$

$\Rightarrow y = 3 x + b \leftarrow is the partial equation$ $rArry=3x+blarrcolor(blue)"is the partial equation"$

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

$using (1, 2) then$ $"using "(1,2)" then"$

$2 = 3 + b \Rightarrow b = 2 - 3 = - 1$ $2=3+brArrb=2-3=-1$

$\Rightarrow y = 3 x - 1 \leftarrow equation in slope-intercept form$ $rArry=3x-1larrcolor(red)"equation in slope-intercept form"$

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How do you write the equation of the line in slope intercept form passing through (1, 2) and (2, 5)?

3 Answers

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