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Graph the Linear Function $y = x - 1$ (Algebra 1)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Graph the line from Part 1, Question 3 ($y = x - 1$) on the provided coordinate grid.
Correct Answer
A line with y-intercept at (0, -1) and slope $1$ (rise 1, run 1)
Detailed Solution Steps
1
Step 1: Identify the y-intercept $b = -1$ from $y = x - 1$. Plot the point (0, -1) on the grid.
2
Step 2: Identify the slope $m = 1$, which is $\\frac{1}{1}$ (rise 1, run 1). From (0, -1), move up 1 and right 1 to plot a second point at (1, 0).
3
Step 3: Draw a straight line connecting (0, -1) and (1, 0), 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
Slope of 1
A slope of 1 means the line has a 1:1 ratio of vertical to horizontal change (rise 1, run 1), creating a 45-degree angle with the x-axis, increasing from left to right.
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