Math Problem Statement

Solve 67

Solve 67: 5x + 2y - 10 = 0

Solution

The equation for question 67 is 5x+2y10=05x + 2y - 10 = 0. Solving for yy, we get:

y=52x+5y = -\frac{5}{2}x + 5

This is in the slope-intercept form y=mx+by = mx + b, where the slope m=52m = -\frac{5}{2} and the y-intercept b=5b = 5.

Would you like to plot the graph or see more details?

Here are five related questions to extend your understanding:

  1. How would you graph the line using the slope-intercept form?
  2. What is the significance of the slope and y-intercept in the equation?
  3. How can we find the x-intercept of this line?
  4. How would the graph change if the equation was 5x+2y+10=05x + 2y + 10 = 0?
  5. What is the relationship between parallel and perpendicular lines for this equation?

Tip: Always check the form of the equation (slope-intercept, point-slope, or standard form) to quickly determine key graphing features like slope and intercepts.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope-intercept form y = mx + b
Standard form Ax + By + C = 0

Theorems

Linear equation theorem

Suitable Grade Level

Grades 9-10