Linear Inequalities in Slope-Intercept Form Flashcard

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert a linear inequality from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y to get y = (-A/B)x + (C/B).

Front

What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the value of y is less than or equal to the expression on the right side of the inequality.

Front

What does the symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the value of y is greater than the expression on the right side of the inequality.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness and direction of the line; a positive slope means the line rises, while a negative slope means it falls.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a dashed line for '<' or '>' and a solid line for '≤' or '≥'. Shade the appropriate region based on the inequality.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation.

Front

Convert the inequality -x + 3y ≤ 9 to slope-intercept form.

Back

y ≤ (1/3)x + 3.

Front

Convert the inequality 4x + 3y ≤ 12 to slope-intercept form.

Back

y ≤ (-4/3)x + 4.

Front

Write the slope-intercept form of the inequality -2x + 5y < 10.

Back

y < (2/5)x + 2.