8.4.A 8.4.C 8.5.B MA.8.AR.3.2 MA.8.AR.3.3 MA.8.AR.3.4 MA.8.AR.3.5 8.5.I

Texas Essential Knowledge and Skills (TEKS) Linear Relationships
Grade:	8th Grade
Standard:	8.4.A
Description:	use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y₂ - y₁)/(x₂ - x₁), is the same for any two points (x₁, y₁) and (x₂, y₂) on the same line;
Standard:	8.4.C
Description:	use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
Standard:	8.5.B
Description:	represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0;
Standard:	MA.8.AR.3.2
Description:	Given a table, graph or written description of a linear relationship, determine the slope.
Standard:	MA.8.AR.3.3
Description:	Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.
Standard:	MA.8.AR.3.4
Description:	Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form.
Standard:	MA.8.AR.3.5
Description:	Given a real-world context, determine and interpret the slope and y-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form.
Standard:	8.5.I
Description:	write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.

A linear function is a function which can be written in the form y = mx + b, where m is the slope and b is where the line crosses the y-axis.

The point where a line crosses the y-axis is called the y-intercept.
At this point, the x-value is 0.

The table, graph, and equation each represent the same line.
The y-intercept of the line is (0, 1).

x	y
-2	-1
-1	0
0	1
1	2

y = x + 1

The slope of a line is also called the rate of change. Given two points on a line, (x_₁, y_₁) and (x_₂, y_₂), the slope is the ratio of the change in y to the change in x.

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

In the equation above, y = x + 1, the slope is the coefficient on x, which is 1.

In the table above, choose any two points to find the slope.
The calculation below shows finding the slope using the points (0, 1) and (1, 2).

\begin{array}{rcl} m & = & \frac{2 - 1}{1 - 0} \\ = & \frac{1}{1} \\ = & 1 \end{array}

In the graph above, choose any two points to find the slope.
The calculation below shows finding the slope using the points (1, 2) and (2, 3).

\begin{array}{rcl} m & = & \frac{3 - 2}{2 - 1} \\ = & \frac{1}{1} \\ = & 1 \end{array}

Texas Essential Knowledge and Skills (TEKS)

Linear Relationships

8.4.A

use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/(x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line;

8.4.C

use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.

8.5.B

represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0;

MA.8.AR.3.2

Given a table, graph or written description of a linear relationship, determine the slope.

MA.8.AR.3.3

Given a table, graph or written description of a linear relationship, write an equation in slope-intercept form.

MA.8.AR.3.4

Given a mathematical or real-world context, graph a two-variable linear equation from a written description, a table or an equation in slope-intercept form.

MA.8.AR.3.5

Given a real-world context, determine and interpret the slope and y-intercept of a two-variable linear equation from a written description, a table, a graph or an equation in slope-intercept form.

8.5.I

write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.

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use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y₂ - y₁)/(x₂ - x₁), is the same for any two points (x₁, y₁) and (x₂, y₂) on the same line;