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)?

• 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#