You don't have to graph a line to understand it. Linear equations represent lines algebraically. These equations possess many different forms, which not only act as graphing outlines but also include important and specific values. One of the most common forms is slope-intercept, where y = mx + b. In this form, "y" and "x" are variables, "m" represents the line's slope and "b" is the y-intercept, the point where the line intersects the y-axis. You can find the y-intercept from the slope-intercept form, or through other linear equation forms like the general and point-slope forms, through simple mathematical operations and substitutions.
Obtain a linear equation in standard or general form, which is a x + b y = c, where "a," "b" and "c" are coefficients. Note that the b-coefficient in this type of equation is different than the b in the slope-intercept form. For this example, allow the equation to be 3x + 5y = -15.
Convert the equation to slope-intercept form by subtracting the expression with the x-variable from each side of the equation, then divide the all expressions by the y-variable's coefficient. In this example, 3x + 5y - 3x = -15 - 3x becomes 5y = -3x -15, and dividing all the terms by 5 results in y = -3/5x - 3.
Set the x-variable to zero and then solve the equation to find the y-intercept. Concluding this example, y = -3/5 * 0 - 3 becomes y = -3. The y-intercept is -3.
Obtain a linear equation in point-slope form, which is (y - y1) = m (x - x1), where "y1" and "x1" are the Cartesian coordinates (x1, y1). For this example, allow the equation to be (y - 2) = 3 (x - 4).
Convert the equation to slope-intercept form by multiplying the slope to the expression in the parentheses and moving the y1 value to the right side of the equation. In this example, (y - 2) = 3 * (x - 4) becomes (y - 2) = 3x - 12, which then becomes y = 3x -10.
Set the x-variable to zero and then solve the equation for the y-intercept. Concluding this example, y = 3 * 0 - 10 becomes y = -10. The y-intercept is -10.
Tips & Warnings
- If the linear equation is given in the form y = m * x + b, just set x to zero and solve.