GRAPHING EQUATIONS & EQUATIONS OF LINESLesson 13.1 & 13.2

STRATEGIES TO GRAPH A LINE

• Make a table.• Special lines• Vertical lines• Horizontal Lines

• Intercepts (x, 0) & (0, y)• Slope-intercept form

MAKE A TABLE & GRAPH 2X – 4Y = 10

x -1 0 1 2

y -3 -5/2 -2 -3/2

SPECIAL LINES:GRAPH Y = 4 & X = -2

y = 4 is a horizontal line where all the y values are 4.

x = -2 is a vertical line where all of the x values are -2.

INTERCEPTSFIND THE X- AND Y- INTERCEPTS FOR THE LINE 2X – 5Y = 10, THEN GRAPH.

X –intercept:What is x when y is zero?2x – 5(0) = 10x = 5 …. (5, 0)

Y-intercept:What is y when x is zero?2(0) – 5y = 10y = -2 … (0, -2)

USE SLOPE-INTERCEPT FORM TO GRAPH THE LINE Y = 2X - 5.

y = mx + b y & x are any point (x, y) that line on

the line. m is the slope b is the y-intercept (0, b)

In the equation y = 2x – 5, m = 2 b = (0, -5)

Graph the y-intercept Graph the slope Connect the dots.

VARIOUS FORMS OF LINEAR EQUATIONS

Slope-Intercept Form (y-form) y = mx + b

Point-Slope Form y – y1 = m(x – x1) m = slope and (x1, y1) is a

known point

Standard Form (General Form) Ax + By = C

THINGS NOT TO FORGET ABOUT LINEAR EQUATIONS

1. Parallel Lines have the SAME slope but different y-intercepts.

2. Perpendicular lines have slopes that are negative reciprocals.

3. Vertical lines have a slope that is undefined.4. Horizontal lines have a slope of zero.5. Midpoint between two points is found using

the formula: x1 + x2 , y1 + y2

2 2