# How do you write an equation of a line with it shows me a graph with a line with points (-1.5,0) and (0,-5)?

Apr 7, 2015
• When we are given the coordinates of any two points on a line, we can use the Point Slope Form to write the equation.

• The Point-Slope form of the Equation of a Straight Line is:
$\left(y - k\right) = m \cdot \left(x - h\right)$
$m$ is the Slope of the Line
$\left(h , k\right)$ are the co-ordinates of any point on that Line.

• To find the Equation of the Line in Point-Slope form, we first need to Determine it's Slope . Finding the Slope is easy if we are given the coordinates of two points.

Slope($m$) = $\frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$ where $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ are the coordinates of any two points on the Line

The coordinates given are $\left(- 1.5 , 0\right)$ and $\left(0 , - 5\right)$

Slope($m$) = $\frac{- 5 - 0}{0 - \left(- 1.5\right)}$ = $\frac{- 5}{1.5}$ = $- \frac{10}{3}$

• Once the Slope is determined, pick any point on that line. Say $\left(0 , - 5\right)$, and Substitute it's co-ordinates in $\left(h , k\right)$ of the Point-Slope Form.

We get the Point-Slope form of the equation of this line as:

color(blue)((y-(-5))=(-10/3)*(x-0)

color(red)(Note:
- If we have to write it in the Slope Intercept form, we just modify the above equation
(The Slope Intercept form is written as $y = m x + c$
where $m$ is the Slope and $c$ is the Y intercept)

$y + 5 = \left(- \frac{10}{3}\right) \cdot x$
color(blue) (y = (-10/3)*x - 5

This is the Slope intercept Form of the equation of the line passing through $\left(- 1.5 , 0\right) \mathmr{and} \left(0 , - 5\right)$

• The graph of the line would look like this:

graph{y =(-10x/3) - 5 [-14.24, 14.24, -7.12, 7.12]}

We can see that the graph has a negative slope, and the Y intercept is $- 5$