Finding X-Intercepts in Linear Equations

Front

What is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept of the equation 2y = 14x + 98?

Back

To find the x-intercept, set y = 0 and solve for x. The equation becomes 0 = 14x + 98, leading to x = -7.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept of the equation 2y = 14x + 98?

Back

To find the y-intercept, set x = 0 and solve for y. The equation becomes 2y = 98, leading to y = 49.

Front

What is the slope of a linear equation in the form y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

How can you determine the slope from the equation 2y = 14x + 98?

Back

Rearranging the equation to slope-intercept form (y = mx + b) gives y = 7x + 49, indicating a slope of 7.

Front

What does it mean for a point to lie on a line represented by a linear equation?

Back

A point (x, y) lies on the line if it satisfies the equation of the line when substituted into it.

Front

How can you verify if the point (-1, 42) lies on the line 2y = 14x + 98?

Back

Substituting x = -1 into the equation gives 2(42) = 14(-1) + 98, which simplifies to 84 = 84, confirming the point lies on the line.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert the equation 2y = 14x + 98 to standard form?

Back

Rearranging gives -14x + 2y = 98, or 14x - 2y = -98.