What is the slope of the line that passes through the points (-2, 5) and (1, 4)

Question

 Math help please

Answer 1

 

The slope of a line is often called "rise over run" because it is the increase in the y-values divided by the increase in the x-values.  A positive slope means a line that goes from lower left to upper right; a negative slope means a line that goes from upper left to lower right; a horizontal line has a slope of 0; and the slope of a vertical line is undefined.

 

Two points determine a line.  That's why you can draw a line given two points.

 

Imagine plotting the points (-2, 5) and (1, 4).  The y-values go from 5 down to 4 while the x-values go from -2 up to 1.  This means that we will have a negative slope.   [special note: we could consider the two points in either order]

 

The points P₁ (x₁, y₁) and P₂ (x₂,y₂) determine a line.  The slope of that line is m=(y₂-y₁)/(x₂-x₁).  [note: the m is the slope when you write the equation in slope-intercept form:  y-mx+b.]

 

    m = (y₂-y₁)/(x₂-x₁)

    m = (4-5)/(1-(-2))

    m = (-1)/(3)

    m = -1/3

 

Get ready for the next step  -- now that you know that m=-1/3 you can use either point to solve this equation for the y-intercept b:

    y = -1/3x + b

Answer 2

Hi Maya, 

To find the slope, we follow these three steps:

Step One: Assign x and y variables to our given points:

(-2, 5) and (1, 4)

(x, y) and (x₂, y₂)

Step Two: Write an equation to relate our variables:

slope=(y₂-y₁)/(x₂-x₁)

Step Three: Plug in our values to solve for slope:

slope=(y2-y1)/(x2-x1)

slope=(4-5)/(1+2) 

slope=(-1)/(3)

slope=-1/3

∴Our slope is -1/3

Best,

Star

 

Answer 3

m = slope

m = (y2-y1)/(x2-x1)

m = (4-5)/(1-(-2))

m = -1/3