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 GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.