Question

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)?

Answer 1

• 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:
  `(y-k)=m*(x-h)`
  `m` is the Slope of the Line
  `(h,k)` 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`) = `(y_2-y_1)/(x_2-x_1)` where `(x_1,y_1)` and `(x_2,y_2)` are the coordinates of any two points on the Line

The coordinates given are `(-1.5,0)` and `(0,-5)`

Slope(`m`) = `(-5-0)/(0-(-1.5))` = `(-5)/1.5` = `-10/3`

• Once the Slope is determined, pick any point on that line. Say `(0,-5)`, and Substitute it's co-ordinates in `(h,k)` 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 = mx + c`
where `m` is the Slope and `c` is the Y intercept)

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

This is the Slope intercept Form of the equation of the line passing through `(-1.5,0) and (0,-5)`

• 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`