Math Problem Statement

determine the gradient and the y-intercept of the line 2x+3y=6

Solution

To determine the gradient (slope) and the y-intercept of the line given by the equation 2x+3y=62x + 3y = 6, we need to rewrite the equation in the slope-intercept form, y=mx+cy = mx + c, where mm is the gradient and cc is the y-intercept.

Steps:

  1. Start with the equation: 2x+3y=62x + 3y = 6

  2. Solve for yy to get the equation into the slope-intercept form: 3y=2x+63y = -2x + 6 y=23x+2y = -\frac{2}{3}x + 2

Results:

  • Gradient (slope) mm: 23-\frac{2}{3}
  • Y-intercept cc: 22

So, the gradient of the line is 23-\frac{2}{3}, and the y-intercept is 22.

Would you like more details or have any questions?


Here are 5 related questions for further practice:

  1. Determine the gradient and y-intercept of the line 4x5y=104x - 5y = 10.
  2. What is the equation of a line parallel to y=23x+4y = -\frac{2}{3}x + 4?
  3. Find the equation of a line that passes through the point (1,3)(1, 3) with a slope of 23-\frac{2}{3}.
  4. Calculate the x-intercept of the line 2x+3y=62x + 3y = 6.
  5. Convert the equation 6x2y=126x - 2y = 12 into slope-intercept form and find its gradient.

Tip: Always convert a linear equation into the slope-intercept form to easily identify the gradient and y-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9