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)?

Question

Kennedy Adams · Accepted Answer

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# 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)# 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#

Eli Assouline · Answer

undefined To write the equation of a line given two points $(-1.5, 0)$ and $(0, -5)$, you can use the point-slope form of a linear equation, which is $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is one of the given points, and $m$ is the slope.

First, find the slope using the formula:

$$m = \frac{y_2 - y_1}{x_2 - x_1}$$

Using the points $(-1.5, 0)$ and $(0, -5)$:

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

Now, choose one of the points, say $(-1.5, 0)$, and plug it along with the slope into the point-slope form:

$$y - 0 = -\frac{10}{3}(x - (-1.5))$$
$$y = -\frac{10}{3}(x + 1.5)$$

You can then distribute and simplify to get the equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.