Writing Equations of Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed 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 from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Tags

CCSS.8.EE.B.5

Front

What is the y-intercept of a linear function?

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

Write the equation of a line with a slope of 3 and a y-intercept of -2.

Back

y = 3x - 2.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

Convert the point-slope form y - 1 = 2(x - 3) to slope-intercept form.

Back

y = 2x - 5.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it forms a straight line, indicating a constant rate of change between the variables.

Tags

CCSS.8.F.A.3

Front

Identify the slope and y-intercept in the equation y = -4x + 7.

Back

Slope: -4, Y-intercept: 7.

Tags

CCSS.8.F.A.3

CCSS.8.EE.B.6

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.