wikiHow Slope and Intercepts of a Line Calculator To calculate the slope and intercepts of a line, you need to have the equation of the line in the form of y = mx + b, where "m" represents the slope and "b" represents the y-intercept. Here are the steps to calculate the slope and intercepts of a line: Identify the equation of the line: Make sure the equation is in the form y = mx + b. If it's not in this form, rearrange the equation to match this form. Determine the slope (m): The slope represents the rate of change of the line. It is the coefficient of the x term in the equation. For example, if the equation is y = 3x + 2, the slope (m) is 3. Determine the y-intercept (b): The y-intercept is the value of y when x is equal to 0. In the equation y = mx + b, the value of b is the constant term. For example, if the equation is y = 3x + 2, the y-intercept (b) is 2. Determine the x-intercept: The x-intercept is the value of x when y is equal to 0. To find the x-intercept, set y to 0 in the equation and solve for x. For example, if the equation is y = 3x + 2, to find the x-intercept, set y = 0 and solve for x. Once you have the slope and intercepts, you can plot the line on a graph or use them to analyze the behavior of the line. Note: In some cases, the equation of the line may not be in the explicit form y = mx + b, but in a different form such as point-slope form or standard form. In such cases, you may need to rearrange the equation or perform additional calculations to determine the slope and intercepts. Example: Consider the equation of a line: y = 2x - 3 Step 1: Identify the equation of the line: The equation is already in the form y = mx + b. Step 2: Determine the slope (m): In this equation, the coefficient of the x term is 2. Therefore, the slope (m) is 2. Step 3: Determine the y-intercept (b): In this equation, the constant term is -3. Therefore, the y-intercept (b) is -3. Step 4: Determine the x-intercept: To find the x-intercept, set y to 0 and solve for x. 0 = 2x - 3 2x = 3 x = 3/2 So, the x-intercept is (3/2, 0). In summary, for the line y = 2x - 3, the slope (m) is 2, the y-intercept (b) is -3, and the x-intercept is (3/2, 0). These values allow us to understand the behavior of the line and make interpretations about its slope and intercepts in relation to the x and y axes. Page