5-5 Vocabulary 8.) x-intercept 9.) Standard form of a linear equation

5-5 Standard Form Algebra 1

Standard Form of a Linear Equation The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, A>= 0, and A and B are not both zero.

Standard Form of a Linear Equation The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, A>= 0, and A and B are not both zero.

Finding an x & y intercept 1.) Substitute 0 for y to find the x value for the x-intercept. 2.) Substitute 0 for x to find the y value for the y-intercept.

Finding an x & y intercept Ex. 1) What are the x- and y- intercepts of the graph of each equation? 1a.) 5x – 6y = 60 1b.) 3x + 4y = 12

Graph a line using intercepts 1.) Find the x- and y- intercepts first. 2.) Then, graph both points. 3.) Connect the dots & extend line with arrows.

Graph a line using intercepts Ex. 2 Graph 2x + 5y = 20

Graphing a line using intercepts Ex. 3 3a.) 3x –7y = 21

Ex. 4 Graphing Horizontal & vertical lines 4a) x = -1 4b) y = 5

5-5B Transforming from standard form to slope intercept form

Standard Form of a Linear Equation The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, A>= 0, and A and B are not both zero.

Slope-Intercept Form The slope-intercept form of an equation of the line is y = mx + b

Ex. 1 Change to slope intercept form 1.) 5x – 6y = 60

Ex. 2 Change to slope intercept form 2.) 3x + 4y = 12

Assignment

Write the equation in Standard Form with integer coefficients Ex. 1a) x + 3y – 4 = 0

*How to change Slope-Intercept Form to Standard Form. y = mx + b Slope-Intercept Form + - mx -mx_____ Adding the Opp. y - mx = b or -mx + y = b Commutative Prop. Of Add. Ax+ By = C Standard Form Be careful of the b,B’s! Lowercase b represents the y-intercept in the Slope-Intercept Form and the uppercase B represents the coefficient of y in the Standard Form.

Write the equation in Standard Form with integer coefficients Ex 1b) y = (5/2)x + 9

Write an equation in standard form of the line that passes through the given point and has the given slope. 2) (-8, 3), m = 2

Write an equation in standard form of the line that passes through the two points 3) (1, 4), (5, 7)

Write an equation in standard form of the horizontal line and the vertical line 4) (1, 3)