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Write Equations Using Point-Slope Formula
We can use another form to write the equation of a line called the Point-Slope formula:
\[y-y_1=m(x-x_1),\] where \((x_1,y_1)\) is a point on the line and \(m\) is the slope.
Using the the points \(( -2, -1)\) and \((3, 2)\) we can write the equation of the line by calculating and slope and then substituting one point into the formula. For simplicity, we choose to use the point: \((3, 2)\).
\[slope=\dfrac{2-(-1)}{-3-(-2)}=\dfrac{2+1}{3+2}=\dfrac{3}{5}\]
\[\begin{align} y-2&=\dfrac{3}{5}(x-3)\\\\ y-2&=\dfrac{3}{5}x-\dfrac{3}{5}(3)\\\\ y-2&=\dfrac{3}{5}x-\dfrac{9}{5}\\\\ y&=\dfrac{3}{5}x-\dfrac{9}{5}+2\\\\ y&=\dfrac{3}{5}x-\dfrac{9}{5}+\dfrac{10}{5}\\\\ y&=\dfrac{3}{5}x+\dfrac{1}{5} \end{align}\]
- Use the Point-Slope formula to write the equation of the line between the points \((0,2)\) and \((-2, -1)\).
- Paper cups of equal size are stacked on a small shelf. You are asked if there is a relationship between the number of stacked cups and the total height of the stack measured in inches from the ground. The table below shows the measurements of the number of stacked cups and their respective heights.
| Number of cups in the stack | Height of the stack (inches) |
| \(3\) | \(2\dfrac{3}{8}\) |
| \(6\) | \(2\dfrac{3}{4}\) |
| \(9\) | \(3\dfrac{1}{8}\) |
| \(12\) | \(3\dfrac{1}{2}\) |
- Show that the relationship between the number of cups in the stack and the stack height is linear.
- Use the Point-Slope formula to write a linear equation to represent this relationship.
- Use words to describe the relationship between the number of stacked cups and the height of the stack from the ground in inches.
For more instruction, go to Watch (Writing Equations using Point-Slope Formula). Close the link to return to this page.
