# What is the slope-intercept form of the line passing through  (-6, 8) and (-1, 7) ?

Slope-intercept form $y = m x + b$ is
$y = - \frac{x}{5} + \frac{34}{5}$

#### Explanation:

Start from the given. Let ${P}_{2} \left(- 6 , 8\right)$ and ${P}_{1} \left(- 1 , 7\right)$

from the given , use the two-point form first
$y - {y}_{1} = \left(\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}\right) \cdot \left(x - {x}_{1}\right)$

after which , transform the equation to $y = m x + b$ slope-intercept form

$y - 7 = \left(\frac{8 - 7}{- 6 - - 1}\right) \cdot \left(x - - 1\right)$

$y - 7 = \frac{1}{- 5} \cdot \left(x + 1\right)$

$- 5 \left(y - 7\right) = - 5 \left(\frac{1}{-} 5\right) \cdot \left(x + 1\right)$

$- 5 \left(y - 7\right) = \cancel{- 5} \left(\frac{1}{\cancel{- 5}}\right) \cdot \left(x + 1\right)$

$- 5 \left(y - 7\right) = 1 \cdot \left(x + 1\right)$

$- 5 y + 35 = x + 1$

$- 5 y = x + 1 - 35$

$- 5 y = x - 34$

$\frac{- 5 y}{-} 5 = \frac{x - 34}{-} 5$

$\frac{\cancel{- 5} y}{\cancel{- 5}} = \frac{x - 34}{-} 5$

$y = - \frac{x}{5} + \frac{34}{5}$

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