# Find The Equation of a Line Through two Points

\( \) \( \)\( \)A step by step worksheet solver to find the equation of a line through two points. As many practice questions as needed may be generated along with their detailed solutions. Solve each step below then click on "Show me" to check your answer. The graph of the line and the two given points are plotted at the bottom of the page in order to gain more understanding of the solution. Step by step solutionSTEP 1: - Check if the two points are distinct. They need to have different $x$-coordinates or different $y$-coordintes or both.
STEP 2: - Find the slope, if possible and say whether the line is vertical, horizontal or neither.
STEP 3: - If the slope found in step (2) is not equal to zero or undefined, use point A (or B) and the slope found in step (2) to find the equation of the line in point-slope form ($y-y_0 = m(x - x_0)$). Write the equation of the horizontal line if the slope is equal to zero, or the equation of the vertical line if the slope is undefined.
STEP 4: - Write the equation of the line in slope intercept form if the slope is defined.
Graphical Meaning of Solution
Below is the graph of the line (blue), and the two points (red) A and B. You may check the slope, the x and y intercepts. |