linear equation slope intercept form calculator

This can be done by substituting the slope and the coordinates of a point (x, y) on the line in the slope-intercept formula and then solve for b. This can be done by calculating the slope between two known points of the line using the slope formula. To summarize how to write a linear equation using the slope-interception form you

Which is the same equation as we got when we read the y-intercept from the graph. If we put in this value for b in the equation we get You can use this equation to write an equation if you know the slope and the y-intercept.Ĭalculate the slope between the two points Where m is the slope of the line and b is the y-intercept. Standard to slope-intercept formĬonverting from standard form to slope-intercept form involves manipulating an equation in standard form so as to isolate y on one side of the equation such that the coefficient on the y is 1.An equation in the slope-intercept form is written as It is relatively common to need to convert the equation of a line in standard or point-slope form to slope-intercept form. It can also be used to write the equation of vertical lines, something that cannot be done using slope-intercept or point-slope form. Standard form is useful when we are trying to solve systems of linear equations. The standard form of the equation of a line is Point-slope form is useful when a point on the line and the slope of the line are known, since it enables us to write an equation for the line. In the equation, y 1 and x 1 indicate a point on the line that is not the y-intercept, while m is the slope. Slope-intercept form is useful because the slope and y-intercept of the line can easily be read off the equation, which also makes it relatively easy to graph the line, since we can just start from the y-intercept and find another point on the line by counting the rise over run (slope) in the coordinate plane. Other commonly used forms include point-slope form and standard form. Depending on the context that a linear equation is being used in, certain forms can be more beneficial to use. Slope-intercept form is just one of a number of different forms of linear equations, albeit it is the most commonly used form. Thus, the y-intercept occurs at the point (0, 3). For example, given the line 3x + 2y = 6, the y-intercept can be found by plugging 0 in for x, then solving for y. It follows that, given an equation, setting x equal to 0 and solving for y will yield the y-intercept of the line. If a graph is given, the point at which the line intersects the y-axis is the y-intercept. The y-intercept can be found in a number of ways. Given at least two points on a line, the slope of the line can be found using the slope formula:įor example, given the that (1, 5) and (-2, 7) are points on the same line, the slope of the line can be found as follows: How to find the slope and the y-intercept Once the slope and y-intercept are known, writing the equation of the line just involves plugging the slope and y-intercept into m and b respectively. We found the y-intercept by plugging the given values into the equation y = mx + b, then solving for b. y = mx + bīecause we are given slope and a point on a line, we just need to find the y-intercept in order to write the equation of the line in slope-intercept form.

Given m = 3 and the point (3, 5), find b, and write the equation of the line in slope-intercept form.

Linear equation slope intercept form calculator