The standard equation is \(y=mx+c\). The forms below lead to this, they just make getting here much faster.
If a pair of coordinates and a gradient is given: \(y-y_1=m(x-x_1)\)
\(x\) and \(y\) remain as-is. \(x_1\) is the x-coordinate provided. \(y_1\) is the y-coordinate provided. \(m\) is the gradient.
If we have point A at (2, 3) on a line with a gradient of 3, here is how we apply this equation:
\(y-3=3(x-2)\)
\(y-3=3x-6\)
\(y=3x-6+3\)
\(y=3x-3\)
There is no fussing around with calculating the the y-intercept, or \(c\) as in the original equation, \(y=mx+c\).
If only two coordinates are given: \(\frac{y-y_1}{y_2-y_1} = \frac{x-x_1}{x_2-x_1}\).
\(x\) and \(y\) remain as-is. The rest of the values are the corresponding \(x\) and \(y\) coordinates provided in the points.
If we have points A at (2, 3) and B at (5, 4):
\(\frac{y-3}{4-3} = \frac{x-2}{5-2}\)
\(y-3 = \frac{x-2}{3}\)
\(3(y-3) = x-2\)
\(3y-9=x-2\)
\(3y=x-2+9\)
\(3y=x+7\)
\(y=\frac{1}{3}x+\frac{7}{3}\)
This article was written on 07/09/2023. If you have any thoughts, feel free to send me an email with them. Have a nice day!