Linear Equations and Transformations

These flashcards cover key concepts related to linear equations, transformations, and properties of geometric figures.

What does the equation 4x + 2y = 40 represent in a word problem about buying drinks and sandwiches?

It represents the total cost where x is the number of sandwiches and y is the number of drinks.

How do you find the slope-intercept form of the equation of a line?

You can convert the equation to the form y = mx + b, where m is the slope and b is the y-intercept.

What is the slope of a line that passes through the points (-3, 0) and (1, 9)?

Slope (m) can be calculated as (y2 - y1) / (x2 - x1), which is (9 - 0)/(1 - (-3)) = 9/4.

How can the point-slope form of a line that passes through (5, 9) with a slope of 7 be expressed?

It can be expressed as y - 9 = 7(x - 5).

What does it mean if a graph represents a proportional relationship?

It means that the ratio between the variables is constant, often represented as a straight line through the origin.

In the context of graphing, what is the significance of the y-intercept?

The y-intercept is the value of y when x is zero and it indicates where the line crosses the y-axis.

What does the slope of a line represent in a real-world context?

The slope represents the rate of change or how one variable changes in relation to another.

Given a triangle's vertices R(-7, 2), S(5, 4), and T(9, -1), what are the transformed coordinates after translating it 1 unit left and 4 units up?

The new coordinates are R'(-8, 6), S'(4, 8), and T'(8, 3).

What is the formula for perimeter P of a rectangle in terms of its length L and width W?

P = 2L + 2W.

What is the type of transformation for a dilation with a scale factor of 2?

It is an enlargement of the figure, increasing the size by a factor of 2.

How can the area A of a rectangle be expressed in terms of length L and width W?

A = L * W.

If a figure is reflected over the y-axis, how do the coordinates of the points change?

The x-coordinates of the points change sign; (x, y) becomes (-x, y).

What does it mean for two triangles to be congruent?

It means all corresponding sides and angles are equal.

How do you set up a proportion to determine the length of a mural if the original photograph measures 3 inches by 5 inches and the width of the mural is 60 inches?

You set up a proportion as 3/5 = 60/x where x is the length of the mural.

In linear equations, what does the term 'parallel lines' refer to?

Parallel lines are lines that have the same slope but different y-intercepts, and they never meet.

What happens to the figure when it is translated 2 units right and 3 units down?

Each point of the figure moves right by 2 units and down by 3 units.