# A line passes through (-7, -5) and (-5, 4). How do you write an equation for the line in point-slope form Rewrite the equation in standard form using integers?

Nov 21, 2016

The equation of the line in slope-intercept form is $y = \frac{9}{2} x + \frac{53}{2.}$
The equation of the line in standard form is $9 x - 2 y = - 53$

#### Explanation:

The slope of the line passing through $\left(- 7 , - 5\right) \mathmr{and} \left(- 5 , 4\right)$ is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{4 + 5}{- 5 + 7} = \frac{9}{2}$

Let the equation of the line in slope-intercept form be $y = m x + c \mathmr{and} y = \frac{9}{2} x + c$ The point (-7,-5) will satisfy the equation . So, $- 5 = \frac{9}{2} \cdot \left(- 7\right) + c \mathmr{and} c = \frac{63}{2} - 5 = \frac{53}{2}$

Hence the equation of the line in slope-intercept form is $y = \frac{9}{2} x + \frac{53}{2.}$

The equation of the line in standard form is $y = \frac{9}{2} x + \frac{53}{2.} \mathmr{and} 2 y = 9 x + 53 \mathmr{and} 9 x - 2 y = - 53$ {Ans]