Number lines - up to 1,000

Learning Objectives Model the evaluation of linear expressions on a number line within the range of 0 to 1,000. Represent the solution sets of linear inequalities on a number line. Calculate the distance between two points on a number line using the absolute value formula. Determine the midpoint between two values on a number line. Visualize the effect of linear transformations (e.g., f(x) = ax + b) on points within the 0 to 1,000 range. Interpret and define intervals on a number line using algebraic notation. If a self-driving car starts at mile marker 200 and travels at 50 mph for 4 hours, how can we visualize its entire journey on a highway map from mile 0 to 1,000? 🚗💨 While you've used number lines before, we'll now elevate that skill to visualize algebraic...

TermDefinitionExample IntervalA continuous set of numbers between two endpoints on a number line. An interval can be open (endpoints not included) or closed (endpoints included).The set of all numbers x such that 150 ≤ x ≤ 400 is a closed interval, represented as [150, 400] on a number line from 0 to 1,000. Solution SetThe set of all values that make an equation or inequality true. On a number line, this is represented by shading the corresponding region.For the inequality x > 750, the solution set is all numbers to the right of 750. On a number line up to 1,000, this would be an open circle at 750 with shading to the right, up to 1,000. Absolute Value (as Distance)The distance of a number from zero on a number line. The distance between two points, 'a' and 'b', is...

Distance Formula on a Number Line D = |b - a| To find the distance (D) between any two points 'a' and 'b' on a number line, subtract one value from the other and take the absolute value of the result. The order of subtraction does not matter due to the absolute value. Midpoint Formula on a Number Line M = \frac{a + b}{2} To find the midpoint (M) between two points 'a' and 'b', add the two values together and divide by 2. This gives you the average position of the two points. Representing Linear Inequalities For ax + b < c, first solve for x. If x < k, use an open circle at k and shade left. If x ≤ k, use a closed circle at k and shade left. The reverse is true for > and ≥. Use an open circle (o) for < and > to sh...