Standard Form & Intercepts

Front

What is the standard form of a linear equation?

Back

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

Front

How do you convert an equation to standard form?

Back

To convert an equation to standard form, rearrange the equation to isolate all terms on one side, ensuring that the coefficients are integers.

Front

What is the x-intercept of a line?

Back

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

Front

What is the y-intercept of a line?

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 x-intercept from an equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

How do you find the y-intercept from an equation?

Back

To find the y-intercept, set x = 0 in the equation and solve for y.

Front

What are intercepts in the context of linear equations?

Back

Intercepts are the points where the graph of the equation intersects the x-axis and y-axis.

Front

What is the significance of the coefficients in the standard form of a linear equation?

Back

The coefficients A and B determine the slope and direction of the line, while C represents the position of the line relative to the origin.

Front

Can the standard form of a linear equation have fractions?

Back

No, the standard form should have integer coefficients. If fractions are present, multiply through by the least common denominator to eliminate them.

Front

What does it mean for a linear equation to be in slope-intercept form?

Back

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.