To graph a line with an equation in slope-intercept form, start by finding one point and slope from the equation.

$calculate slope intercept form$

Substitute the coordinates (x 1, y 1) and (x 2, y 2) for the two points in the slope formula, then solve for m.Īfter you have solved for m, you can use it along with one of the points to find the y-intercept and put the equation of the line in slope-intercept form following the steps above. The first step to do this is to find the slope using the slope formula we showed above. If you have two points on a line, then you can also find the slope-intercept form. X = c How to Find Slope-Intercept Form for Two Points

Since vertical lines have an undefined slope, they cannot be represented using slope-intercept form.īut, a vertical line is commonly expressed as x = c, where c is the x-intercept and also x-coordinate of any point on the line. The y-coordinate is always equal to the y-intercept.Ī vertical line is a line that runs parallel to the y-axis, and since it has infinite steepness, the slope is undefined. If you simplify this to remove the 0x portion, the result is:Īnd that’s the equation of a horizontal line in slope-intercept form. So, let’s substitute 0 for m in the slope-intercept form equation. A horizontal line runs parallel to the x-axis and has a slope of 0, meaning it has no steepness at all. You can also use slope-intercept form to express a horizontal line. Y = 1 / 2x + 7 / 2 Slope-Intercept Form for a Horizontal Line Then, express the line in slope-intercept form using the slope of 1/2 and the y-intercept of 7/2. Since we know the slope, we can start with the second step and input 1/2 for the m variable, 5 for the x variable, and 6 for the y variable to solve for b using slope-intercept form. The result is the equation of the line in slope-intercept form.įor example, let’s create the equation for a line with a slope of 1/2 and a point (5, 6) in slope-intercept form. Now, input the slope and y-intercept for the m and b variables in the slope-intercept form equation. Step Three: Express the Line in Slope-Intercept Form You can also find b using a y-intercept calculator. Input the slope and coordinates for a known point on the line for the m, x, and y variables, respectively, in the slope-intercept form equation. If you know the slope already, then you can skip this step. If you know two points on the line, you can use the slope formula above to find it or use a slope calculator. The first step is to find the line’s slope. You can express the equation of a straight line in slope-intercept form in a few steps. Then, since point (x 2, y 2) is an arbitrary point on the line, we can rename it to just (x, y).įinally, we see that the resulting equation of the line is the slope-intercept form equation above. Now, we can substitute the y-intercept (which, by definition, is the coordinate (0, b)) for (x 1, y 1). If you multiply both sides of this equation by the denominator (x 2 – x 1), the formula can be rewritten as: The formula for slope using the coordinates for two points (x 1, y 1) and (x 2, y 2) is: Slope-intercept form is derived from the slope formula. In the slope-intercept formula, the slope of the line m is the coefficient for the x-coordinate, and the y-intercept is represented as the b variable. The slope-intercept form of a line states that the y-coordinate y of a point on the line is equal to the slope m times the x-coordinate x plus the y-intercept b. The slope-intercept form equation is given by: The y-intercept is the y-coordinate where the line crosses the y-axis. Slope-intercept form is applicable when you have the slope and y-intercept for a line or when you can calculate these for the line. The combination of these elements can be used to plot any point on the line. Slope-intercept form gets its name because the equation contains the slope and the y-intercept of the line. The slope-intercept form equation can be used to find any point on the line. Slope-intercept form is a type of linear equation format used to express a straight line. Slope-intercept form is probably the most frequently used equation format to represent a line, but you can also express the line in point-slope form or standard form. You can use a calculator like the one above to find the equation for a straight line in slope-intercept form, but you can also follow the steps below to find it. The most commonly used method is an algebraic equation in slope-intercept form. There are several ways to describe a line using its slope, or gradient.

Calculate slope intercept form