Question

What is the slope of the line that passes through points (-3,4) and (2,-5)

Answer 1

`\large\boldsymbol{\rm{Slope}}`

`\bf{Intro}`

A line's slope is the rate of change. It's calculated as:

`\rm\quad m = (\Delta x)/(\Delta y)`

But there's another formula for calculating the slope, and that is the slope formula:

`\mapsto\quad\rm{m=(y_2-y_1)/(x_2-x_1)`

Where:

• m = slope
• 
  `\rm{x_1}` is the x-coordinate of the first point
• 
  `\rm{x_2}` is the x-coordinate of the second point
• 
  `\rm{y_1}` is the y-coordinate of the first point
• 
  `\rm{y_2}` is the y-coordinate of the second point

We can take any two points on the graph, plug them into the slope formula, and get the slope.

In this case, we're given the points (-3,4) and (2,-5), so we go ahead and substitute the values into the formula:

`\rm{y=(-5-4)/(2-(-3))}`

Simplify.

`\rm{y=(-9)/(2+3)}`

`\rm{y=(-9)/(5)}`

`\rm{y=-(9)/(5)}`

✦ Therefore, the slope is -9/5.

`\rule{350}{1}`

Answer 2

Answer:
`-(9)/(5)`

Explanation:

We can use the slope formula to find the slope of this line. This formula finds the change in y over the change in x.

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) ) =(-5-4)/(2--3)=(-9)/(2+3) =-(9)/(5)`