AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Graph the Linear Function $y = \\frac{4}{3}x$ (Algebra 1 Practice)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Graph the line from Part 1, Question 4 ($y = \\frac{4}{3}x$) on the provided coordinate grid.
Correct Answer
A line passing through the origin (0,0) with slope $\\frac{4}{3}$ (rise 4, run 3)
Detailed Solution Steps
1
Step 1: Identify the y-intercept $b = 0$ from $y = \\frac{4}{3}x$, so the line passes through the origin (0, 0). Plot (0, 0) on the grid.
2
Step 2: Identify the slope $m = \\frac{4}{3}$ (rise 4, run 3). From (0, 0), move up 4 and right 3 to plot a second point at (3, 4).
3
Step 3: Draw a straight line connecting (0, 0) and (3, 4), 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
Linear Functions Passing Through the Origin
When the y-intercept $b = 0$, the linear equation is written as $y = mx$, and the line passes through the origin (0,0). These are called proportional linear functions, where y is directly proportional to x.
Loading solution...
