Solving in both forms <ul><li>A.Write the equation in point slope form of the line with slope 4 that passes through the point (4,-3). B.Then solve the equation for y </li></ul>y-(-3) = 4(x-4) Substituting the values into the euation y+3 = 4(x-4) This is Point Slope Form. Apply the distributive property for the parentheses. This will give us the slope intercept form. (The equation is solved for y.) -3 -3 y= 4(x-4) -3 y= 4x-16-3 <ul><li>y-y 1 = m(x-x 1 ) </li></ul>(slope intercept form) Y=4x-19 y 1 x 1
Example Write the point slope form of the equation of the line with slope of -4 that passes through (2,5). Then solve for y.
If you are given two points and you need to write an equation in point-slope form, then you can use either point for (x 1 ,y 1 ).
Example Write the point slope form of the equation of the line that passes through (2,5) and (-1,0). Then solve for y.
The Slope-Intercept Form of the Equation of a Line
Two forms for Equations of Lines Slope Intercept Form For a nonvertical line with slope m and y-intercept b the equation is y=mx+b Example: slope =2 y-intercept of 6 Y=2x +6 Point Slope Form For a nonvertical line with slope m that passes through (x 1 ,y 1 ) the equation is y-y 1 = m(x-x 1 ) Example: slope = -3 point on the line(-1,-2) Y-(-2)= -3(x-(-1)) Y+2= -3(x+1)
Graph the linear equation y= 2/3x+4 First: Plot the y-intercept of 4 Rise by 2 units Run ( go to the right) by 3 units. Plot the second point (3, 6) Connect the two points with a straight edge or ruler. (0,4) (3,6)