Math Problem Statement
What is the equation of the line that passes through the point left parenthesis, minus, 2, comma, minus, 8, right parenthesis(−2,−8) and has a slope of 1?
Solution
To find the equation of a line that passes through the point and has a slope of , we use the point-slope form of the equation of a line, which is:
where is the slope, and is a point on the line.
Step 1: Substitute the given values
Here, , , and . Substituting these into the point-slope form gives:
which simplifies to:
Step 2: Simplify the equation
Expanding the right-hand side:
Subtract 8 from both sides to solve for :
Thus, the equation of the line is:
Would you like more details or have any questions about this process?
Here are 5 related questions to deepen your understanding:
- How do you convert from point-slope form to slope-intercept form?
- What is the equation of a line with a slope of 2 passing through the point (3, 4)?
- How do you find the slope of a line given two points?
- How would the equation change if the slope were instead of ?
- What is the significance of the slope in the equation of a line?
Tip: The slope-intercept form of a line equation is , where is the slope and is the y-intercept.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Point-Slope Form
Slope-Intercept Form
Formulas
Point-slope form: y - y1 = m(x - x1)
Slope-intercept form: y = mx + b
Theorems
Slope formula
Suitable Grade Level
Grades 8-10
Related Recommendation
Find the Equation of a Line Through (-2, 8) with Slope -1
Equation of Line Passing Through Point (-6, -8) with Slope 1/2
Find the Equation of a Line with Slope -8 through (9, -8)
Equation of a Line with Slope -2 Passing Through (4, -8)
Find the Equation of a Line with Point (-1, -8) and Slope 5 in Slope-Intercept Form