Question

rate of change
slope
on a linear graph, this is called the
slope is written as a of the vertical change
to the horizontal change between any two points on a line.
this remains for any two points on the same line.
slope is written as a m
variable for slope
types of slope
finding slope on a graph
directions: find the slope of each line. write your answer in simplest form

Explanation:

Step1: Recall slope formula

The slope $m$ of a line is given by the ratio $m=\frac{\text{vertical change}}{\text{horizontal change}}=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: For an upward - sloping line (left - to - right)

If we have a line that rises from left to right, the vertical change (rise) and horizontal change (run) are both non - zero. For example, if we pick two points $(x_1,y_1)$ and $(x_2,y_2)$ on an upward - sloping line where $x_2>x_1$ and $y_2 > y_1$, then $m=\frac{y_2 - y_1}{x_2 - x_1}>0$.

Step3: For a downward - sloping line (left - to - right)

If the line falls from left to right, if we pick two points $(x_1,y_1)$ and $(x_2,y_2)$ with $x_2>x_1$ and $y_2

Step4: For a horizontal line

For a horizontal line, the $y$ - values of all points on the line are the same. So if we take two points $(x_1,y)$ and $(x_2,y)$ on a horizontal line, then $m=\frac{y - y}{x_2 - x_1}=0$.

Step5: For a vertical line

For a vertical line, the $x$ - values of all points on the line are the same. If we take two points $(x,y_1)$ and $(x,y_2)$ on a vertical line, then the denominator in the slope formula $x_2 - x_1 = 0$. Since division by zero is undefined, the slope of a vertical line is undefined.

Answer:

The slope of a line is the ratio of the vertical change to the horizontal change between any two points on the line. It is constant for any two points on the same line and is denoted by the variable $m$. A line that rises from left - to - right has a positive slope, a line that falls from left - to - right has a negative slope, a horizontal line has a slope of 0, and a vertical line has an undefined slope.