QQuestionMathematics
QuestionMathematics
"Part A
What kind of line would you use to graph the linear inequality: y≤2x−4?
Part B
Where would you shade the solutions to the linear inequality: y≤2x−4?"
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Answer
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Step 1:I'll solve this problem step by step, following the specified LaTeX formatting guidelines:
Part A: Type of Line for $$y \leq 2x - 4
Step 2:: Identify the Line Type
- This is a linear inequality in slope-intercept form: $$y = mx + b
- Here, m = 2 (slope) and b = - 4 (y-intercept) - This represents a straight line with a slope of 2 and a y-intercept of - 4
Step 3:: Determine Line Characteristics
- This is a solid line because of the $$\leq$$ symbol (less than or equal to)
- The line has a positive slope of 2, which means it rises from left to right Part B: Shading Solutions
Step 4:: Understand Inequality Shading
- For $$y \leq 2x - 4$$, we shade the region below and on the line
- This means all points with y-coordinates less than or equal to the line's value
Step 5:: Shading Procedure
- Draw the line $$y = 2x - 4$$ as a solid line
- Shade the entire region below this line, including the line itself - This represents all points that satisfy the inequality
Final Answer
- Part A: A straight line with slope 2 and y-intercept - 4 - Part B: Shade the entire region below and including the line y = 2x - 4
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