2-4 MORE ABOUT LINEAR EQUATIONS

Write an equation of a line by using the slope and a point on the line.

Point-Slope Form

Uses one point, (x1, y1) on a line to create an equation

Writing an Equation

A line passes through (-3, 6) and has a slope of -5.

= m() Plug in the slope an d point = -5() y – 6 = -5(x + 3)

Graphing

y – 1 = (x – 2) We know the slope is And it passes through the point (2, 1)

Standard Form of a Linear Equation So far we have learned how to write

linear equations in slope-intercept form and point-slope form.

Standard form is written Ax + By = C where A, B, and C are real numbers

Intercepts

The x-intercept is the x-coordinate of a point where a graph crosses the x-axis.Found where the y-value is 0

Find x and y intercepts of the graph of 3x + 4y = 24

Sub 0 for y to find x-interceptX =8

Sub 0 for x to find y-interceptY = 6

Graphing Using Intercepts What is the graph of x – 2y = -2? Find intercepts

X = -2Y = 1

Write as ordered pairs(-2, 0)(0, 1)

Plot the ordered pairs

Horizontal and Vertical Lines x = 3 Write in standard form: 1x + 0y = 3

y = 3 Standard form: 0x + 1y = 3

Transforming to Standard Form

What is y = in standard form Get rid of fractions by multiplying by 7 7y = 7() Distribute: 7y = -3x + 35 Add 3x: 7y + 3x = 35 Done! These equations, though they look

different, are equivalent.

Parallel Lines

Lines in the same plane that never intersect.

Nonvertical lines are parallel if they have the same slope and different y-intercepts.

Vertical lines are parallel if they have different x-intercepts.

Ex: Same slope, different y-intercept

Perpendicular lines Lines that intersect to form right angles

Two nonvertical lines are perpendicular if the product of their slopes is -1.The slope is the opposite reciprocal.Ex: the opposite reciprocal of is since their

product is -1. A vertical line and a horizontal line are

always perpendicular.