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# Graphing Linear Equations

Goals

• Understand that lines represent solutions of linear equations.
• Graph linear equations.
• Find slopes of lines using two points.
• Find slopes of lines from tables.
• Find slopes and y-intercepts of graphs of linear equations.
• Graph linear equations written in slope-intercept form.
• Graph linear equations written in standard form.
• Write equations of lines in slope-intercept form.
• Write equations of lines using slope and a point.
• Write equations of lines using two points.

Vocabulary

• linear equation
• solution of a linear equation slope
• rise
• run
• perpendicular lines
• x- intercept
• y- intercept
• slope-intercept form
• standard form point-slope form

Concepts

Linear Equations

• A linear equation is an equation whose graph is a line.
• The points on the line are solutions of the equation.

Graphing Horizontal and Vertical Lines

• The graph of y = b is a horizontal line passing through (0, b).
• The graph of x = a is a vertical line passing through (a, 0).

Slope

The slope of a line is a ratio of the change in y (the rise) to the change in x (the run) between any two points, (x1, y1) and (x2, y2), on the line.

Parallel Lines and Slopes

• Two different lines in the same plane that never intersect are parallel lines. Nonvertical parallel lines have the same slope.
• All vertical lines are parallel.

Perpendicular Lines and Slopes

• Two lines in the same plane that intersect to form right angles are perpendicular lines. Two nonvertical lines are perpendicular if and only if the product of their slopes is –1.
• Vertical lines are perpendicular to horizontal lines.

Intercepts

• The x-intercept of a line is the x-coordinate of the point where the line crosses the x-axis. It occurs when y = 0.
• The y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis. It occurs when x = 0.

Slope-Intercept Form

A linear equation written in the form
y = mx + b is in slope-intercept form.
The slope of the line is m and the y-intercept of the line is b.

Standard Form of a Linear Equation

The standard form of a linear equation is ax + by = c, where a and b are not both zero.

Point-Slope Form

A linear equation written in the form
y – y1 = m(x – x1) is in point-slope form. The line passes through the point (x1, y1) and the slope of the line is m.