Math Problem Statement
Graph this line: y - 5 = (1/5)(x - 1).
Solution
Let's analyze the equation of the line provided:
This equation is in point-slope form, which is:
where is the slope, and is a point on the line. From the equation:
- The slope () is ,
- The point is .
Steps to Graph the Line:
-
Plot the point as given in the equation.
-
Use the slope (rise over run):
- Rise = (move up by 1 unit),
- Run = (move right by 5 units).
Starting from , moving 5 units right and 1 unit up takes you to .
-
Plot this second point .
-
Draw a straight line through these two points.
Key Points to Plot:
- — starting point.
- — using the slope.
Would you like me to explain more details about graphing? Let me know!
Related Questions:
- What is the slope-intercept form of this equation?
- How do you convert from point-slope form to slope-intercept form?
- What happens to the graph if the slope is negative?
- How do you determine if two lines are parallel or perpendicular?
- How do you find the x-intercept of this line?
Tip:
When graphing using slope, always move from one point using "rise over run" to plot additional points. This ensures accuracy!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing Lines
Point-Slope Form
Slope
Formulas
y - y₁ = m(x - x₁)
Slope = Rise/Run
Theorems
Concept of Slope-Point Form
Slope Formula
Suitable Grade Level
Grades 8-10