Graphing Using Intercepts

Front

What is the x-intercept of the equation x + 4y = 7?

Back

The x-intercept is the point where the graph crosses the x-axis, which occurs when y = 0. For the equation x + 4(0) = 7, the x-intercept is (7, 0).

Front

What are the x-intercepts of the graph of the equation 3x + 4y = 24?

Back

To find the x-intercepts, set y = 0. The equation becomes 3x + 4(0) = 24, which simplifies to x = 8. Thus, the x-intercept is (8, 0).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is written as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you graph the equation x + y = 3?

Back

To graph the equation, find the intercepts. Set x = 0 to find the y-intercept (0, 3) and set y = 0 to find the x-intercept (3, 0). Plot these points and draw a line through them.

Front

What is the definition of an intercept in graphing?

Back

An intercept is a point where a graph crosses an axis. The x-intercept is where the graph crosses the x-axis, and the y-intercept is where it crosses the y-axis.

Front

What is the y-intercept of the equation 2x + 3y = 6?

Back

To find the y-intercept, set x = 0. The equation becomes 2(0) + 3y = 6, which simplifies to y = 2. Thus, the y-intercept is (0, 2).

Front

How can you convert an equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the slope of the line represented by the equation 4x - 2y = 8?

Back

To find the slope, convert to slope-intercept form: -2y = -4x + 8, then y = 2x - 4. The slope (m) is 2.

Front

What does it mean for an equation to be in standard form?

Back

An equation is in standard form if it is expressed as Ax + By = C, where A, B, and C are integers, and A is non-negative.

Front

How do you find the y-intercept of the equation 5x + 2y = 10?

Back

Set x = 0 in the equation: 5(0) + 2y = 10, which simplifies to y = 5. The y-intercept is (0, 5).