Integrated Math 1 Final Review

Front

Does the graph show a function?

Back

A graph represents a function if every input (x-value) has exactly one output (y-value). If a vertical line intersects the graph at more than one point, it is not a function.

Front

Write the equation of the line with a slope of 6 that goes through the point (-3,7).

Back

The equation of a line in slope-intercept form is given by: y = mx + b, where m is the slope and b is the y-intercept. To find b, substitute the point (-3, 7) into the equation: 7 = 6(-3) + b, which gives b = 25. Thus, the equation is y = 6x + 25.

Front

If Dexter pays $8.90 for his hamburger, how many toppings did he get?

Back

To find the number of toppings, we need to know the cost of the hamburger and the cost per topping. Assuming the base price of the hamburger is $5.90 and each topping costs $1, we can set up the equation: 5.90 + 1t = 8.90, where t is the number of toppings. Solving gives t = 3.

Front

Solve the equation: 3x - 3 = 2x + 6.

Back

To solve for x, first isolate x on one side: 3x - 2x = 6 + 3, which simplifies to x = 9.

Front

What is the slope of the line through the points (-6,8) and (2,24)?

Back

The slope (m) of a line through two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1). Here, m = (24 - 8) / (2 - (-6)) = 16 / 8 = 2.

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a graph, or an equation.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way to express the equation of a line as y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a line?

Back

To find the y-intercept of a line, set x = 0 in the equation of the line and solve for y.

Front

What does it mean for a graph to be linear?

Back

A graph is linear if it can be represented by a straight line. This means the relationship between the variables is proportional and can be described by a linear equation.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the one that is changed or controlled in an experiment, while the dependent variable is the one that is measured or affected.