AI Math Solver
Resources
Questions
Pricing
Login
Register
Home
>
Questions
>
Graph the Linear Function $y = -x + 2$ (Algebra 1 Practice)
Mathematics
High School Grade 9 (Algebra 1)
Question Content
Graph the line from Part 1, Question 2 ($y = -x + 2$) on the provided coordinate grid.
Correct Answer
A line with y-intercept at (0, 2) and slope $-1$ (rise -1, run 1 or rise 1, run -1)
Detailed Solution Steps
1
Step 1: Identify the y-intercept $b = 2$ from $y = -x + 2$. Plot the point (0, 2) on the grid.
2
Step 2: Identify the slope $m = -1$, which can be written as $\\frac{-1}{1}$ (rise -1, run 1) or $\\frac{1}{-1}$ (rise 1, run -1). From (0, 2), move down 1 and right 1 to plot a second point at (1, 1).
3
Step 3: Draw a straight line connecting (0, 2) and (1, 1), 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
Negative Slope
A negative slope means the line decreases from left to right. It can be represented as a negative rise (moving down) with a positive run (moving right), or a positive rise (moving up) with a negative run (moving left).
Loading solution...
