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 , we need to rewrite the equation in the slope-intercept form, , where is the gradient and is the y-intercept.
Steps:
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Start with the equation:
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Solve for to get the equation into the slope-intercept form:
Results:
- Gradient (slope) :
- Y-intercept :
So, the gradient of the line is , and the y-intercept is .
Would you like more details or have any questions?
Here are 5 related questions for further practice:
- Determine the gradient and y-intercept of the line .
- What is the equation of a line parallel to ?
- Find the equation of a line that passes through the point with a slope of .
- Calculate the x-intercept of the line .
- Convert the equation 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