# How do you write an equation in SLOPE-INTERCEPT form of the line passing through the given points (2, 7), (1, -4)?

Apr 16, 2016

$y = 11 x - 15$

#### Explanation:

The slope-intercept form is $y = m x + c$, where $m$ is the slope and $c$ is the $y$-intercept.

The slope is given by the change in $y$ divided by the change in $x$,

$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 4 - 7}{1 - 2} = 11$

which gives us

$y = 11 x + c$.

Now substitute in values for $x$ and $y$ from the points given to find $c$.

$- {4}_{y} = 11 \cdot {1}_{x} + c$
$c = - 15$

and put this back into the equation

$y = 11 x - 15$

Apr 16, 2016

$y = 11 x - 15$

#### Explanation:

Slope intercept formula: $y = m x + b$
1) find the slope of the two points by using the formula:
$\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 4 - 7}{1 - 2} = \frac{- 11}{-} 1 = 11$

We now have so far: $y = 11 x + b$

We can use a sample coordinate to find the value of b or the y-intercept (the place where the line crosses the y-axis).

We can use (2,7) where $7 = y$ and $2 = x$.
$7 = 11 \left(2\right) + b$

Solve for b.
$7 = 11 \left(2\right) + b$
$7 = 22 + b$
$7 - 22 = 22 - 22 + b$
$- 15 = b$

Slope-intercept form: $y = 11 x - 15$