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Linear Equations Exploration
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Linear Equations Exploration
For each question, show your thinking when it helps. Use y = mx + b to identify slope and y-intercept.
Reading Linear Equations
1.In the equation y = mx + b, which statement correctly describes m and b?
- m is the slope; b is the y-intercept.
- m is the y-intercept; b is the slope.
- m is the x-value; b is the y-value.
2.For y = 4x − 3, identify the slope.
- −3
- 4
- 1
3.For y = −2x + 9, what is the y-intercept?
x
y
0
−2
1
1
2
4
3
7
Equations in Context
4.At a coding club, a robot kit costs $6 to rent plus $4 for each hour of use. Write an equation for the total cost y after x hours.
5.Using the robot kit rental details above, find the cost for 7 hours of use.
6.A coding club charges $18 per month for access and a one-time setup fee of $12. In y = 18x + 12, where x is the number of months and y is the total cost, explain what the slope and y-intercept mean.
7.Match each equation with its description.
- y = 6x + 4
- y = −3x + 7
- y = 0.25x
- The line increases gently and passes through the origin.
- The line decreases from left to right and crosses the y-axis at 7.
- The line increases steeply and crosses the y-axis at 4.
Slope and Graphs
8.Choose every statement that is true about the slope of a line.
- A positive slope means the line rises from left to right.
- A negative slope means the line falls from left to right.
- A positive slope always makes a line steeper than a negative slope.
- The y-intercept determines whether the slope is positive or negative.
9.Create a linear equation in the form y = mx + b and describe a real situation it could represent. State what x and y mean.
Draw a straight line that represents your equation from the previous question.
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