LINEAR EQUATIONS

LINEAR EQUATIONS

By Susan Brown

WHAT ARE LINEAR EQUATIONS?

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has a variable whose exponent is more than 1. The graph of a linear equation always forms a straight line.

Linear Equation Definition: A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear' equation.

There are linear equations in one variable and linear equations in two variables. Let us learn how to identify linear equations and non-linear equations with the help of the following examples.

WHAT ARE LINEAR EQUATIONS?

Equations	Linear or Non-Linear
y = 8x - 9	Linear
y = x2 - 7	Non-Linear, the power of the variable x is 2
√y + x = 6	Non-Linear, the power of the variable y is 1/2
y + 3x - 1 = 0	Linear

Linear Equations

Graphing Linear Equations

Linear Graph

• An equation whose graph is a line is a linear equation.

• You can plot points on a coordinate plane to graph a linear equation.

• Example: y = -4x + 4.

Linear Equations Review

Slope-Intercept Form

Point-Slope Form

Standard Form

Parallel & Perpendicular Lines

X and Y Intercepts

• Linear equations have x and y-intercepts. 

• The x-intercept is the x-coordinate of the point at which the graph crosses the x-axis.

• The y-intercept is the y-coordinate of the point at which the graph crosses the y-axis. 

Slope-Intercept: y = mx+b

• Used for graphing linear equations

• Need a slope (m) and y-intercept (b)

Multiple Choice

What is the x-intercept of the graph?

• (5,0)

• (0,5)

• (0,4)

• (4,0)

Multiple Choice

Find the equation that corresponds to the graph.

• y = -3/4x + 4

• y = 4/3x + 4

Multiple Choice

What is the y-intercept?

• (0,15)

• (3,0)

• (15,0)

• (0,3)

Point-slope Form: y - y₁ = m( x - x₁)

• Useful when you are given a point (x₁, y₁) and slope (m)

• Plug in the opposite values of points into formula

Multiple Choice

What is the y-intercept?

• (2,0)

• (0,2)

• (0,-2)

• (-2,0)

Multiple Choice

Given m = 3 and (-2 , 5) write the equation in point-slope form.

• y + 5 = 3 (x - 2)

• y - 5 = 3 (x + 2)

Graphing an Equation

• You need only 2 points to graph a line.

• You can choose a value for x, and then evaluate for y.

Standard Form : Ax + By = C

• Form is useful to convert to a different form.

• A, B, and C are all whole numbers.

Make a Table of Values or T-Chart

• Choose a value for x, plug in, and solve for y.

• Do this 2 or 3 times.

• Then, use the points to graph your equation.

Multiple Choice

Convert the following standard form equation to slope-intercept (y=mx+b).

• 2y = -6x + 24

• y = -3x + 12

Build a t-chart

• The Red Arrow shows y=-4 after simplifying.

• The Green Arrow shows y=0 after simplifying.

• The Yellow Arrow shows y=4 after simplifying.

Parallel Lines : Slopes are the same

Perpendicular Lines : Opposite Reciprocal slopes

Use point-slope and then convert to slope-intercept.

Graph

• Plot each ordered pair.

• Connect with a line.

• The points were (0,-4), (2,0), (4,4)

Multiple Choice

Write the equation of the line parallel to y = 3x - 4/3 through the point (-1, 2) in slope-intercept form.

• y - 2 = 3 (x +1)

• y = 3x + 5

• y = 3x + 1

Fill in the Blanks

If x = 2, in the equation y = 3x - 5, what is the value of y?

Fill in the Blanks

What is the slope of the line that is perpendicular to y = 3/4x + 5/3?

Do not type any spaces

Fill in the Blanks

If x = 0, in the equation y = -2x - 4, what is the value of y?

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If x = -2, in the equation y = -3x - 10, what is the value of y?

Fill in the Blanks

If x = -6, in the equation y = 5x + 7, what is the value of y?

Fill in the Blanks

If x = 4, in the equation x + y = -12, what is the value of y?

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If x = -3, in the equation -2x + y = 15, what is the value of y?

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If x = 4, in the equation y = -5x, what is the value of y?

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If x = 5, in the equation 5x + y = 20, what is the value of y?