A linear equation is an equation that represents a straight line when graphed on a coordinate plane. The general form of a linear equation in one variable is: *y = mx + b*, where *y* represents the dependent variable, *x* represents the independent variable, *m* is the slope, and *b* is the y-intercept.

The slope-intercept form of a linear equation is *y = mx + b*. The slope (*m*) represents the rate of change of the line, and the y-intercept (*b*) represents the point where the line intersects the y-axis.

The point-slope form of a linear equation is *y - y _{1} = m(x - x_{1})*. This form is useful when you know the slope and a point on the line.

The standard form of a linear equation is *Ax + By = C*, where *A*, *B*, and *C* are constants. This form is useful for graphing and finding the x and y-intercepts.

To graph a linear equation, you can use the slope-intercept form to identify the y-intercept and slope, or you can use the x and y-intercepts if the equation is in standard form.

To solve a linear equation, you can use various methods such as substitution, elimination, or graphing. The goal is to isolate the variable (*x* or *y*) to find its value.

- Understand the different forms of linear equations: slope-intercept form, point-slope form, and standard form.
- Be able to identify the slope and y-intercept from the equation in slope-intercept form.
- Practice graphing linear equations and finding the x and y-intercepts.
- Practice solving linear equations using various methods.
- Understand the relationship between the equation of a line and its graphical representation.

Remember to always check your solutions by substituting the values back into the original equation to ensure they satisfy the equation.

Study GuideLinear equations Worksheet/Answer key

Linear equations Worksheet/Answer key

Linear equations Worksheet/Answer key

Linear equations Worksheet/Answer keyLinear equations Worksheet/Answer keyLinear equations Worksheet/Answer keyLinear equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.

Grade 8 Curriculum Focal Points (NCTM)

Algebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations

Students use linear functions, linear equations, and systems of linear equations to represent, analyze, and solve a variety of problems. They recognize a proportion (y/x = k, or y = kx) as a special case of a linear equation of the form y = mx + b, understanding that the constant of proportionality (k) is the slope and the resulting graph is a line through the origin. Students understand that the slope (m) of a line is a constant rate of change, so if the input, or x-coordinate, changes by a specific amount, a, the output, or y-coordinate, changes by the amount ma. Students translate among verbal, tabular, graphical, and algebraic representations of functions (recognizing that tabular and graphical representations are usually only partial representations), and they describe how such aspects of a function as slope and y-intercept appear in different representations. Students solve systems of two linear equations in two variables and relate the systems to pairs of lines that intersect, are parallel, or are the same line, in the plane. Students use linear equations, systems of linear equations, linear functions, and their understanding of the slope of a line to analyze situations and solve problems.

Connections to the Grade 8 Focal Points (NCTM)

Geometry: Given a line in a coordinate plane, students understand that all 'slope triangles' - triangles created by a vertical 'rise' line segment (showing the change in y), a horizontal 'run' line segment (showing the change in x), and a segment of the line itself - are similar. They also understand the relationship of these similar triangles to the constant slope of a line.