Find the x and y-intercepts of an equation in standard form.
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Standard form: Ax + By = C
To find the x-intercept:
Set y = 0: This is because the x-intercept is the point where the line crosses the x-axis, and at any point on the x-axis, the y-coordinate is 0.
Solve for x: Once you've set y = 0, solve the resulting equation for x. The value of x you find is the x-intercept.
To find the y-intercept:
Set x = 0: This is because the y-intercept is the point where the line crosses the y-axis, and at any point on the y-axis, the x-coordinate is 0.
Solve for y: Once you've set x = 0, solve the resulting equation for y. The value of y you find is the y-intercept.
Example:
Consider the equation 2x + 3y = 6.
To find the x-intercept:
Set y = 0: 2x + 3(0) = 6
Solve for x: 2x = 6
x = 3
So, the x-intercept is (3, 0).
To find the y-intercept:
Set x = 0: 2(0) + 3y = 6
Solve for y: 3y = 6
y = 2
So, the y-intercept is (0, 2).
Remember: The x-intercept is the point where the line crosses the x-axis, so the y-coordinate is always 0. Similarly, the y-intercept is the point where the line crosses the y-axis, so the x-coordinate is always 0.
To find the x-intercept:
Set y = 0: This is because the x-intercept is the point where the line crosses the x-axis, and at any point on the x-axis, the y-coordinate is 0.
Solve for x: Once you've set y = 0, solve the resulting equation for x. The value of x you find is the x-intercept.
To find the y-intercept:
Set x = 0: This is because the y-intercept is the point where the line crosses the y-axis, and at any point on the y-axis, the x-coordinate is 0.
Solve for y: Once you've set x = 0, solve the resulting equation for y. The value of y you find is the y-intercept.
Example:
Consider the equation 2x + 3y = 6.
To find the x-intercept:
Set y = 0: 2x + 3(0) = 6
Solve for x: 2x = 6
x = 3
So, the x-intercept is (3, 0).
To find the y-intercept:
Set x = 0: 2(0) + 3y = 6
Solve for y: 3y = 6
y = 2
So, the y-intercept is (0, 2).
Remember: The x-intercept is the point where the line crosses the x-axis, so the y-coordinate is always 0. Similarly, the y-intercept is the point where the line crosses the y-axis, so the x-coordinate is always 0.
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