Modeling Linear Equations

What does it mean for a line to be horizontal?

• A horizontal line has a slope of 0 and can be represented by the equation y = a constant value.

• A horizontal line has an undefined slope and can be represented by the equation x = a constant value.

• A horizontal line rises from left to right and has a positive slope.

• A horizontal line has a slope of 1 and can be represented by the equation y = mx + b.

How can you graph a linear equation?

• Find the y-intercept, plot it on the graph, and use the slope to find another point, then draw a line through the points.

• Identify the x-intercept and connect it to the origin.

• Use a table of values to plot points and connect them with a curve.

• Draw a vertical line at the y-intercept and extend it indefinitely.

What is the equation of a line with a slope of 2 that passes through the point (1, 3)?

• y = 2x + 1

• y = 2x - 1

• y = 3x + 2

• y = x + 3

What does it mean for a line to have a negative slope?

• A line with a negative slope increases as it moves from left to right, indicating that as x increases, y increases.

• A line with a negative slope decreases as it moves from left to right, indicating that as x increases, y decreases.

• A line with a negative slope is horizontal, indicating that y remains constant as x increases.

• A line with a negative slope is vertical, indicating that y increases or decreases without any change in x.

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

• y = mx + b

• y - y1 = m(x - x1)

• y = y1 + m(x - x1)

• y - y1 = b(x - x1)

What is the significance of the delivery fee in the holiday meal cost equation?

• It is a variable cost that increases with the number of people.

• It is a fixed cost that does not change with the number of people, represented as the y-intercept in the equation y = 30 + 12.5x.

• It is an optional cost that can be waived during promotions.

• It is a cost that only applies to large orders over a certain number of people.

How can you determine if two lines are parallel?

• Two lines are parallel if they have the same slope but different y-intercepts.

• Two lines are parallel if they intersect at a right angle.

• Two lines are parallel if they have different slopes.

• Two lines are parallel if they are both horizontal.

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

• m = (y2 - y1) / (x2 - x1)

• m = (x2 - x1) / (y2 - y1)

• m = (y1 + y2) / (x1 + x2)

• m = (y1 - y2) / (x2 - x1)

What is a linear equation?

• A linear equation is an equation that makes a straight line when graphed.

• A linear equation is an equation that forms a curve when graphed.

• A linear equation is an equation that has no solutions.

• A linear equation is an equation that only contains whole numbers.

What does it mean for a line to be vertical?

• A vertical line has an undefined slope and can be represented by the equation x = a constant value.

• A vertical line has a slope of zero and runs parallel to the x-axis.

• A vertical line has a defined slope and can be represented by the equation y = mx + b.

• A vertical line is a line that intersects the y-axis at a specific point.