IM Unit 3 Review: Linear Relationships

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

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

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is the value of y when x is 0, represented by the 'b' in the equation y = mx + b.

Front

How do you write an equation for a line given a slope and a point?

Back

Use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Front

What is the difference between a function and a non-function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value). A non-function can have an input that corresponds to multiple outputs.

Front

How can you determine if a relation is a function from a graph?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What does the equation y = 4 represent on a graph?

Back

The equation y = 4 represents a horizontal line that crosses the y-axis at 4. It indicates that for every value of x, y will always be 4.

Front

What does the equation y = -2x + 4 represent on a graph?

Back

The equation y = -2x + 4 represents a line with a slope of -2 and a y-intercept of 4. It decreases as x increases.

Front

How do you interpret the cost equation 0.5p + 4b = 15?

Back

In this equation, p represents the number of pencils and b represents the number of boxes of pencils. The equation shows the total cost of buying pencils and boxes of pencils must equal $15.

Front

What is the total cost for Mark's internet plan after one month?

Back

The total cost after one month is $350, which includes a $300 startup fee and $50 for the first month.