by gingersnap0819 on Thu Feb 28, 2013 7:18 am
y = mx + b is slope-intercept form, not point-slope form. The point-slope formula is y - y_{1} = m(x - x_{1}), where you will most likely be given a point (x_{1}, y_{1}) and a slope (m) that you can then substitute into the formula by replacing those variables with the numbers you were given in the problem.
For example, if you were asked to write an equation of a line in point-slope form, given the point P(2, -3) and the slope of the line is 4, you would substitute the number 2 into the formula to replace x_{1}, the number -3 into the formula to replace y_{1}, and the number 4 into the formula to replace m:
y - (-3) = 4(x - 2) which would then simplify to give: y + 3 = 4x - 8. You may then be asked also to manipulate the equation into other forms such as slope-intercept form (y = mx + b) or Standard Form (Ax + By = C). To convert to slope-intercept form, solve the equation for y and make sure that the x-term is listed before the constant term on the other side of the equation. Continuing with the previous example, you would subtract 3 from both sides of the equation to get y = 4x - 11, and from this equation you can see that m (slope) is 4- and it better be since that's what we were given in the first place! and b (the y-intercept) is -11, so the graph of this line crosses the y-axis (vertical axis) at -11.