![]() Ratio = “rise over run”, or vertical over horizontal # = ((-6)/1) = -6# for the slope, m.Ī line has the general form of y = mx + b, or vertical position is the product of the slope and horizontal position, x, plus the point where the line crosses (intercepts) the x-axis (the line where z is always zero.) So, once you have calculated the slope you can put any of the two points known into the equation, leaving us with only the intercept 'b' unknown. In this form, the coefficient of x (m) is the slope. Slope-Intercept Form: The most straightforward way to find the slope is if the equation is already in slope-intercept form, which is y mx + b. Horizontal difference “x” # = x_2 – x_1 = -2 – -3 = 1# The general formula for slope-intercept form is y mx + b, where m represents the slope of the line, and b represents the y-. There are a few ways to find the slope of an equation, depending on the form of the equation and your needs. Thus, for any two points defined by Cartesian (planar) coordinates such as those given in this problem, you simply set up the two changes (differences) and then make the ratio to obtain the slope, m. Y = mx + b Calculate the slope, m, from the given point values, solve for b by using one of the point values, and check your solution using the other point values.Ī line can be thought of as the ratio of the change between horizontal (x) and vertical (y) positions. Where #color(red)(m)# is the slope and #color(blue)(b)# is the y-intercept value. The slope-intercept form of a linear equation is: #y = color(red)(m)x + color(blue)(b)# Now, solve for #y# to put the equation in slope-intercept form. This form allows you to quickly write the equation without needing the y-intercept. #(y - color(red)(1)) = color(blue)(-6)(x + color(red)(3))# The equation of a line in the point-slope form is y-y1mleft(x-x1right) Example: Given a line passing through the point (2,5) with a slope of 3, its equation in the point-slope form is y-53(x-2). Substituting the slope we calculated and the first point gives: Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through. The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))# Next, we can write an equation in point-slope form. Substituting the values from the points in the problem gives: Slope intercept form calculator uses slope m and y-intercept b to find the equation of a line in the two-dimensional Cartesian coordinate plane. ![]() Where #m# is the slope and ( #color(blue)(x_1, y_1)#) and ( #color(red)(x_2, y_2)#) are the two points on the line. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# ![]() First, we need to determine the slope of the line passing through these two points.
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