![]() ![]() 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.Ħ = ( 1 / 2 × 5) + b 6 = 5 / 2 + b 6 – 5 / 2 = 5 / 2 + b – 5 / 2 b = 7 / 2 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. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |