Lofton-Haynes

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 * Definition**: The point slope form of the equation of a nonvertical line that passes through the points (x1,y1) and has slope m is : y-y1= m(x-x1)

// // **Changing From Point-Slope to Slope y-intercept Form:**

y// – //y//1 = //m//(//x// – //x//1) //y - y//1 //= mx - mx 1 y - y//1 + //y//1 = //mx - mx 1 + y//1 //y = mx - mx//1 //+ y//1 or //y = m//(//x - x//1) + //y//1

Point-Slope Form can be used to find the Slope y-intercept equation by using a known point on the line and the slope.

ex. (-1,-6) m=4

y - y1 = m(x - x1) y - (-6) = 4(x - [-1]) y + 6 = 4(x + 1) y + 6 = 4x + 4 y + 6 - 6 = 4x + 4 - 6 y = 4x - 2


 * ex. ** You can always find the slope(m) when given two points, for example (-2, 4)(1,2)

//m//=__(4)-(2)= 2=__ _ __2__ (-2)-(1)=-3= 3

Then you can use either of the points and the slope to plug into point-slope form. m= _ __2__ (//x//1, //y//1)= (–2, 4) 3

//y// – //y//1 = //m//(//x// – //x//1) //y// – (4) = ( – 2/3 )(//x// – (–2)) //y// – 4 = ( – 2/3 )(//x// + 2) //y// – 4 = ( – 2/3 ) //x// – 4/3 //y// = ( – 2/3 ) //x// – 4/3 + 4 //y// = ( – 2/3 ) //x// – 4/3 + 12/3 **//y// = ( – 2/3 ) //x// + 8/3**