# What is the slope, y-intercept and equation for the line that passes through these points: (-1, -8), (-6, -33), (-10, -53) and (-13, -68)?

Aug 3, 2018

Equation of the line in slope-intercept form is $y = 5 x - 3$ and y intercept is $y = - 3$

#### Explanation:

The slope of the line passing through

$\left(- 1 , - 8\right) \mathmr{and} \left(- 6 , - 33\right)$ is

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 33 + 8}{- 6 + 1} = \frac{- 25}{-} 5 = 5$

Let the equation of the line in slope-intercept form be

$y = m x + c \mathmr{and} y = 5 x + c$ , the point (-1,-8) will satisfy

the equation . $\therefore - 8 = 5 \cdot \left(- 1\right) + c \mathmr{and} c = - 8 + 5 = - 3$

Therefore , y intercept is $y = - 3$

Hence the equation of the line in slope-intercept form is

$y = 5 x - 3$ . Check for points $\left(- 10 , - 53\right) \mathmr{and} \left(- 13 , - 68\right)$

on the line , $y = 5 x - 3 \therefore - 53 = 5 \cdot \left(- 10\right) - 3$ or

$- 53 = - 53 \mathmr{and} - 68 = 5 \cdot \left(- 13\right) - 3 \mathmr{and} - 68 = - 68$

Therefore all for points satisfy the equation of line.

Equation of the line in slope-intercept form is $y = 5 x - 3$ and

y intercept is $y = - 3$

graph{5 x-3 [-10, 10, -5, 5]} [Ans]