Create Linear Equations from Various Representations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Tags

CCSS.8.EE.B.5

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the rate of change (slope) between any two points is constant.

Tags

CCSS.HSF-LE.A.1B

Front

What is the equation of a line that passes through the points (1, 1) and (3, 5)?

Back

y = 2x - 1.

Front

What does the term 'rate of change' mean in a linear function?

Back

Rate of change refers to how much the output (y) changes for a unit change in the input (x). In a linear function, this is constant.

Tags

CCSS.HSF-LE.A.1B

Front

Write the equation for a linear function with a slope of 3 and a y-intercept of -2.

Back

y = 3x - 2.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the equation for the cost of renting a paddleboat with a $7 initial fee and $3.50 per hour?

Back

y = 3.5x + 7.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

How do you convert a word problem into a linear equation?

Back

Identify the variables, determine the relationship between them, and express it in the form of y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2