What is the equation of the line passing through $(1, 3), (4, 6)$ $(1,3), (4,6)$ ?

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What is the equation of the line passing through $(1, 3), (4, 6)$ $(1,3), (4,6)$ ?

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Answer 1 · 2018-03-20T13:23:27

$y = x + 2$ $y=x+2$

Explanation:

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

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

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

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

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

$let (x_{1}, y_{1}) = (1, 3) and (x_{2}, y_{2}) = (4, 6)$ $"let "(x_1,y_1)=(1,3)" and "(x_2,y_2)=(4,6)$

$\Rightarrow m = \frac{6 - 3}{4 - 1} = \frac{3}{3} = 1$ $rArrm=(6-3)/(4-1)=3/3=1$

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

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

$using (1, 3) then$ $"using "(1,3)" then"$

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

$\Rightarrow y = x + 2 \leftarrow is the equation of the line$ $rArry=x+2larrcolor(red)"is the equation of the line"$

Answer 2 · 2018-03-20T13:33:00

$y = x + 2$ $y=x+2$

Explanation:

First, we must know what an equation of a line looks like. We write the equation in slope-intercept form:

$y = m x + b$ $y=mx+b$
(The $m$ $m$ is the slope, and $b$ $b$ is the y-intercept)

Next, find the slope ( $m$ $m$ ) of the line by using the formula $\frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $(y_2-y_1)/ (x_2-x_1)$ :

$\frac{(6) - (3)}{(4) - (1)}$ $((6)-(3))/((4)-(1))$ $=$ $=$ $\frac{3}{3}$ $3/3$ $=$ $=$ $1$ $1$

Next, find the y-intercept ( $b$ $b$ ) by using the slope-intercept form equation and substituting $1$ $1$ in for $m$ $m$ and one of the ordered pairs in for $x$ $x$ and $y$ $y$ :

$(3) = (1) (1) + b$ $(3)=(1)(1)+b$ $\to$ $->$ $3 = 1 + b$ $3=1+b$ $\to$ $->$ $2 = b$ $2=b$
-OR-
$(6) = (1) (4) + b$ $(6)=(1)(4)+b$ $\to$ $->$ $6 = 4 + b$ $6=4+b$ $\to$ $->$ $2 = b$ $2=b$

Now, we can write the full equation of the line:

$y = x + 2$ $y=x+2$
(We do not need to put a $1$ $1$ in front of $x$ $x$ because we know that $1$ $1$ times any number equals itself)

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What is the equation of the line passing through $(1, 3), (4, 6)$ $(1,3), (4,6)$ ?

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What is the equation of the line passing through $(1, 3), (4, 6)$ $(1,3), (4,6)$ ?