Standard form and Point-slope form of linear equations Define and use the standard form of a linear equation. Define and use the point-slope form of a linear equation.

Standard Form of a linear equation: Ax + By = C In this form, the x and y are on one side of the equal sign and the constant ( the number without the variable) is one the other side. Generally, A, the coefficient of x, is written as a POSITIVE WHOLE NUMBER. An equation in slope-intercept form can be converted into standard form: y = -6x+8  Slope-intercept form. The y is by itself with a coefficient of 1. 6x+y = 8  Standard form. The x and y are on one side. x has a positive whole number coefficient

Point Slope form: y - y1 = m(x - x1) You plug the values of the coordinates of a given point into the x1 & y1 spots and the slope into the m spot. Write an equation in point slope form for a line that has a slope of 4 and contains the point (-3, 8) y - y1 = m(x - x1) y - 8 = 4(x - -3) y - 8 = 4(x + 3)

Write an equation in point slope form for the line that contains (5,-2) & (-2,5) y1 - y2 x1 - x2 -2-5 5- -2 = -7 7 =-1 Step 1) find the slope: Step 2) use that slope you found and either one of the points and plug it into the equation y - y1 = m(x - x1) y - 5 = -1(x - -2) y - 5 = -1(x +2) y - y1 = m(x - x1) y - -2 = -1(x - 5) or y + 2 = -1(x -5)

But are these equations the same? y - 5 = -1(x +2) y + 2 = -1(x -5) Get them into slope-intercept form to see if they are the same y - 5 = -1(x +2) y-5 =-x-2 y=-x+3 y + 2 = -1(x -5) y+2=-x+5 y=-x+3 Or get them into standard form to see if they are the same y - 5 = -1(x +2) y-5 = -x-2 x+y-5 = -2 x+y = 3 y + 2 = -1(x -5) y+2=-x+5 x+y+2 = 5 x+y = 3

Find the x- & y-intercepts for the graph of the equation: 4x-5y=20 Since it is not in slope-intercept form you cannot just read the y-intercept. You must solve the problem twice. Plug in a zero, one at a time, for each variable. 4x-5y=20 4x-5y=20 4(0)-5y=20 4x-5(0)=20 -5y=20 4x =20 x=5 y= -4 y-intercept is (0,-4) x-intercept is (5,0)