The slope-intercept form of a linear equation is written as:

y = mx + b

Where:

**y**is the y-coordinate of a point on the line.**x**is the x-coordinate of a point on the line.**m**is the slope of the line.**b**is the y-intercept of the line, which is the point where the line crosses the y-axis.

To write an equation in slope-intercept form, you need to find the slope (*m*) and the y-intercept (*b*).

The slope (*m*) is the ratio of the vertical change (*rise*) to the horizontal change (*run*) between two points on the line. It can be calculated using the formula:

m = (y_{2} - y_{1}) / (x_{2} - x_{1})

The y-intercept (*b*) is the value of *y* when *x* is 0. You can find it by looking at the point where the line crosses the y-axis or by substituting *x* = 0 into the equation of the line and solving for *y*.

Let's say we have two points on a line: (2, 5) and (4, 11). We can find the slope and y-intercept of the line using the formula for slope and the given points.

First, we find the slope:

m = (11 - 5) / (4 - 2) = 6 / 2 = 3

Next, we find the y-intercept. We can use the point (2, 5) and the slope-intercept form equation:

y = mx + b

5 = 3(2) + b

b = 5 - 6 = -1

So the equation of the line in slope-intercept form is:

y = 3x - 1

- Understand the meaning of slope and y-intercept in the context of linear equations.
- Practice finding the slope and y-intercept given two points on a line.
- Learn how to use the slope-intercept form to graph a line.
- Practice converting an equation from standard form to slope-intercept form.
- Work on real-world problems that involve using the slope-intercept form of a linear equation.

Remember, the slope-intercept form is a powerful tool for understanding and working with linear equations, and it's important to practice applying it to different situations.

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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.