Slope-intercept form is useful when we know the y- intercept of a line. However, we are not always given this information. When we know the slope and one point which is not the y-intercept, we can write the equation in point-slope form.
Equations in point-slope form look like this:
|y - k = m(x - h)|
To write an equation in point-slope form, given a graph of that equation, first determine the slope by picking two points. Then pick any point on the line and write it as an ordered pair (h, k). It does not matter which point you pick, as long as it is on the line--different points yield different constants, but the resulting equations will describe the same line.
Finally, write the equation, substituting numerical values in for m, h, and k. Check your equation by picking a point on the line--not the point you chose as (h, k)--and confirming that it satisfies the equation.
Example 1: Write an equation of the following line in point-slope form:
Example 2: Write an equation of the line which passes through (3, 4) and has slope m = 5.
h = 3 and k = 4. y - 4 = 5(x - 3)