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Graph the Linear Function $y = \\frac{3}{2}x - 5$ (Algebra 1)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Graph the line from Part 1, Question 5 ($y = \\frac{3}{2}x - 5$) on the provided coordinate grid.
Correct Answer
A line with y-intercept at (0, -5) and slope $\\frac{3}{2}$ (rise 3, run 2)
Detailed Solution Steps
1
Step 1: Identify the y-intercept $b = -5$ from $y = \\frac{3}{2}x - 5$. Plot the point (0, -5) on the grid.
2
Step 2: Identify the slope $m = \\frac{3}{2}$ (rise 3, run 2). From (0, -5), move up 3 and right 2 to plot a second point at (2, -2).
3
Step 3: Draw a straight line connecting (0, -5) and (2, -2), extending it across the grid.
Knowledge Points Involved
1
Graphing Linear Equations from Slope-Intercept Form
To graph a line from $y = mx + b$, first plot the y-intercept $(0, b)$, then use the slope $m = \\frac{rise}{run}$ to find a second point, and connect the points with a straight line. This is the most straightforward method for graphing linear functions.
2
Fractional Slope
A fractional slope $\\frac{rise}{run}$ means the vertical change (rise) and horizontal change (run) are not whole-number units. Use the numerator for vertical movement and denominator for horizontal movement to find additional points on the line.
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