Equations of Lines and Graphing Them

Equations of Lines Vertical line x = # Horizontal line y = # Slope, y-intercept y=mx+b Standard Form Ax+By = C using intercepts Standard Form using magic

COORDINATE PLANE Parts of a plane 1.X-axis 2.Y-axis 3.Origin 4.Quadrants I-IV X-axis Y-axis Origin ( 0, 0 ) QUAD IQUAD II QUAD IIIQUAD IV

Slope-Intercept form of a line

SLOPE Review Slope is the ratio of the vertical rise to the horizontal run between any two points on a line. Usually referred to as the rise over run. Slope triangle between two points. Notice that the slope triangle can be drawn two different ways. Rise is -10 because we went down Run is -6 because we went to the left Rise is 10 because we went up Run is 6 because we went to the right

SLOPE-INTERCEPT FORM OF A LINE The slope intercept form of a line is y = mx + b “m” represents the slope “b” represents the y-intercept. ♥ When an equation is in slope-intercept form the “y” is always on one side by itself. ♥ If a line is not in slope-intercept form, then we must solve for “y” to get it there.

Write the equation of the line with a y-intercept of 3 and a slope of 2 Then…. graph it. y = 2x + 3 First step Second step Third step – draw the line

IN SLOPE-INTERCEPTNOT IN SLOPE-INTERCEPT y = 3x – 5y – x = 10 y = -2x + 102y – 8 = 6x y = -.5x – 2y + 4 = 2x Put y – x = 10 into slope-intercept form Add x to both sides and would get y = x + 10 Put 2y – 8 = 6x into slope-intercept form. Add 8 to both sides then divide by 2 and would get y = 3x + 4 Put y + 4 = 2x into slope-intercept form. Subtract 4 from both sides and would get y = 2x – 4.

The x-intercept is point where graph touches (or crosses) the x-axis. The y-intercept is point where graph touches (or crosses) the y-axis. 1. To find x-intercepts, let y be zero and solve the equation for x. 2. To find y-intercepts, let x be zero and solve the equation for y. Finding Intercepts of an Equation

X AND Y INTERCEPTS The x-intercept is the x-coordinate of a point where the graph crosses the x-axis. The y-intercept is the y-coordinate of a point where the graph crosses the y-axis. The x-intercept would be 4 and is located at the point (4, 0). The y-intercept is 3 and is located at the point (0, 3).

The Intercepts Y-Intercept = 6 X-Intercept = 2 The intercepts are where the line crosses the axis.

Finding the intercepts 3x + y = 6 To find the x-intercept, let y = 0 3x + (0) = 6 3x = 6

Finding the intercepts 3x + y = 6 To find the y-intercept, let x = 0 3(0) + y = 6

The graph of 3x + y = 6 x-intercept = 2 y-intercept = 6

Finding the intercepts x + 5y = 10 find the x-intercept x + 5(0) = 10 x = 10 find the y-intercept 0 + 5y = 10 5y = 10 y = 2 The coordinates are (10, 0) and (0, 2)

The graph of x + 5y = 10 x-intercept = 10 y-intercept = 2

1.Find your x-intercept: Let y = 0 -2x + 3(0) = 12 x = -6; (-6, 0) 2.Find your y-intercept: Let x = 0 -2(0) + 3y = 12 y = 4; (0, 4) 3.Graph both points and draw a line through them. Graphing with intercepts: -2x + 3y = 12

Find the intercepts and graph 3x + 4y = 12 x = 4 y = 3 Coordinates are: (4, 0) and (0, 3)

The graph of 3x + 4y = 12 x-intercept = 4 y-intercept = 3

Find the intercepts and graph y = 4x - 4 move the 4x -4x + y = -4 GO! x = 1 y = -4 Oh, no! What now?

Writing and Graphing using Standard Form of a line

Write the equation in Standard Form: Ax + By = C y = 2x + 3 Get your variables on one side of the equation and the constant on the other. -2x + y = 3 You’re not done…. the coefficient of x must be a positive integer. 2x – y = -3

Write the equation in Standard Form: Ax + By = C y = 2/5x - 3 Get your variables on one side of the equation and the constant on the other. -2/5x + y = -3 Check the coefficient of x. Guess we’re not done yet. Multiply the equation by -5 2x – 5y = 15

Write the equation in Standard Form: Ax + By = C y = 2/5x - 3 OR…. You recognize that the coefficient of x needs work: Multiply the equation by 5. 5y = 2x - 3 Move the variables to one side: -2x + 5y = -15 Multiply by -1 2x – 5y = 15

Graphing a line from Standard Form Using Magic Slope = -A B x - intercept =C A y - intercept =C B Ax + By = C

2x – y = -3 For example: Slope = -A B x - intercept =C A y - intercept =C B Slope = -2 = 2 -1 x - intercept =-3 2 y - intercept =-3 = 3 Knowing this can set up your equation to graph in EITHER slope-intercept form or graphing by intercepts!!

Here’s your cheat sheet!