Slope of a line

The slope tells you how much $y$ increases when $x$ increases by 1. From two points $(x_1,\,y_1)$ and $(x_2,\,y_2)$,

For example, for $(3,\,1)$ and $(5,\,-3)$ it is $\dfrac{-3-1}{5-3}=\dfrac{-4}{2}=-2$.

When the slope is known and one $y$-coordinate is □, use change in $y$ $=$ slope $\times$ change in $x$. For $(3,\,-2)$ and $(6,\,\square)$ with slope 2, $x$ increases by 3, so $y$ increases by 6 and $\square=-2+6=4$.

Examples

1. 01What is the slope of the line through these two points?$\displaystyle (2,\ -4),\quad (3,\ -3)$AnswerHide

   Answer$\displaystyle 1$
2. 02The line through these two points has slope 2. What goes in □?$\displaystyle (3,\ -2),\quad (6,\ \square)$AnswerHide

   Answer$\displaystyle 4$
3. 03The line through these two points has slope -3. What goes in □?$\displaystyle (1,\ -4),\quad (3,\ \square)$AnswerHide

   Answer$\displaystyle -10$
4. 04What is the slope of the line through these two points?$\displaystyle (3,\ 1),\quad (5,\ -3)$AnswerHide

   Answer$\displaystyle -2$
5. 05The line through these two points has slope -2. What goes in □?$\displaystyle (-1,\ 4),\quad (2,\ \square)$AnswerHide

   Answer$\displaystyle -2$
6. 06What is the slope of the line through these two points?$\displaystyle (-1,\ -5),\quad (2,\ -8)$AnswerHide

   Answer$\displaystyle -1$

FAQ

Q1Which point do I subtract from?AnswerHide

A

Either, as long as you subtract in the same order on top and bottom: $\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{y_1-y_2}{x_1-x_2}$. Mixing the order between top and bottom flips the sign.

Q2What if $x_1=x_2$?AnswerHide

A

The denominator is 0, so the slope is undefined. The line is the vertical line $x=x_1$, parallel to the $y$-axis.