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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)