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Graph the Linear Function $y = \\frac{1}{4}x - 1$ (Algebra 1)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Graph the line from Part 1, Question 1 ($y = \\frac{1}{4}x - 1$) on the provided coordinate grid.
Correct Answer
A line with y-intercept at (0, -1) and slope $\\frac{1}{4}$ (rise 1, run 4)
Detailed Solution Steps
1
Step 1: Identify the y-intercept $b = -1$ from the slope-intercept form $y = \\frac{1}{4}x - 1$. Plot the point (0, -1) on the coordinate grid.
2
Step 2: Identify the slope $m = \\frac{1}{4}$, which means a rise of 1 unit up and a run of 4 units to the right. From the y-intercept (0, -1), move up 1 and right 4 to plot a second point at (4, 0).
3
Step 3: Draw a straight line connecting the two points (0, -1) and (4, 0), extending it to cover 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 as Rise Over Run
Slope $m$ is defined as $\\frac{rise}{run}$, where rise is the vertical change (positive = up, negative = down) and run is the horizontal change (positive = right, negative = left). This is used to find additional points on a line when graphing.
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