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

Apr 20, 2018

y = 3x -1

#### Explanation:

1. Find the slope by using the formula $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
You wil get: $\frac{5 - 2}{2 - 1}$
Simplify to get 3

2. 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

1. Answer is y = 3x -1
Apr 20, 2018

$y = 3 x - 1$

#### Explanation:

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

$\implies$ $\frac{5 - 2}{2 - 1}$ =$\frac{3}{1}$ =3

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

Use (1,2) $\implies$ $2 = 3 \times 1 + c$
$\implies$ $2 = 3 + c$ so $c$=-1

this gives $y = 3 x - 1$

Apr 20, 2018

$y = 3 x - 1$

#### Explanation:

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

•color(white)(x)y=mx+b

$\text{where m is the slope and b the y-intercept}$

$\text{to calculate m use the "color(blue)"gradient formula}$

•color(white)(x)m=(y_2-y_1)/(x_2-x_1)

$\text{let "(x_1,y_1)=(1,2)" and } \left({x}_{2} , {y}_{2}\right) = \left(2 , 5\right)$

$\Rightarrow m = \frac{5 - 2}{2 - 1} = 3$

$\Rightarrow y = 3 x + b \leftarrow \textcolor{b l u e}{\text{is the partial equation}}$

$\text{to find b substitute either of the 2 given points into}$
$\text{the partial equation}$

$\text{using "(1,2)" then}$

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

$\Rightarrow y = 3 x - 1 \leftarrow \textcolor{red}{\text{equation in slope-intercept form}}$