The slope-intercept form of a line reveals a lot of information.
Linear equations can take several forms. The standard form is aX + bY = c, where a, b and c are numbers. The formula when you know two points, (X1, Y1) and (X2, Y2), is Y - Y1 = (Y1 - Y2)X / (X1 - X2). When the slope m and a point (X1, Y1) are known, the formula is Y - Y1 = m(X - X1). A form that is often preferred is the slope-intercept form Y = mX + b, where b is the place that the line intercepts the Y axis.
Instructions
1. Find the slope of the line, computing it from any two points (X1, Y1) and (X2, Y2) on the line. The slope m = (Y1 - Y2) / (X1 - X2). Notice that it does not matter in which order you choose the points, because (Y1 - Y2) / (X1 - X2) = (Y2 - Y1) / (X2 - X1).
2. Find the slope intercept form using the slope and one point. The point-slope form is Y -Y1 = m(X - X1). If you know that the slope is 1/2 and the line goes through point (2, 3), the point-slope allows us to write: Y - 3 = 1/2(X - 2) or Y -3 = 1/2X - 1. This means that the slope intercept form is Y = 1/2X + 2.
3. Get the Y-axis intercept from the slope intercept form. If the slope intercept form is Y = mX + b, then b is the point where the line crosses the Y axis. Therefore, if the line that goes through the point (2, 3) and has slope 1/2 has the slope-intercept form Y = 1/2X + 2, then this line crosses the Y axis at the point (0, 2). A line with the formula Y = mX + b intercepts the Y axis at b.
Tags: intercept form, slope intercept, slope intercept form, slope-intercept form, crosses axis