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 (2,8)(-2, -8) and has a slope of m=1m = 1, we use the point-slope form of the equation of a line, which is:

yy1=m(xx1)y - y_1 = m(x - x_1)

where mm is the slope, and (x1,y1)(x_1, y_1) is a point on the line.

Step 1: Substitute the given values

Here, m=1m = 1, x1=2x_1 = -2, and y1=8y_1 = -8. Substituting these into the point-slope form gives:

y(8)=1(x(2))y - (-8) = 1(x - (-2))

which simplifies to:

y+8=1(x+2)y + 8 = 1(x + 2)

Step 2: Simplify the equation

Expanding the right-hand side:

y+8=x+2y + 8 = x + 2

Subtract 8 from both sides to solve for yy:

y=x6y = x - 6

Thus, the equation of the line is:

y=x6y = x - 6

Would you like more details or have any questions about this process?

Here are 5 related questions to deepen your understanding:

  1. How do you convert from point-slope form to slope-intercept form?
  2. What is the equation of a line with a slope of 2 passing through the point (3, 4)?
  3. How do you find the slope of a line given two points?
  4. How would the equation change if the slope were 1-1 instead of 11?
  5. What is the significance of the slope in the equation of a line?

Tip: The slope-intercept form of a line equation is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.

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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