Writing Linear Equations: Check for Understanding

Front

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

Back

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

Front

How do you identify the slope and y-intercept from the equation y = -2x + 5?

Back

In the equation y = -2x + 5, the slope (m) is -2 and the y-intercept (b) is 5.

Front

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

Back

The point-slope form of a linear equation is given by the formula y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you convert the equation 5x - 2y = 12 into slope-intercept form?

Back

To convert 5x - 2y = 12 into slope-intercept form, solve for y: 2y = 5x - 12, then y = (5/2)x - 6.

Front

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

Back

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

Front

How do you find the slope between two points, such as (-2, -3) and (4, 3)?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1). For (-2, -3) and (4, 3), m = (3 - (-3)) / (4 - (-2)) = 6/6 = 1.

Front

What is the y-intercept of the linear function f(x) = -2x - 2?

Back

The y-intercept of the function f(x) = -2x - 2 is -2, which is the value of f(0).

Front

How can you write a linear equation given a slope and a point?

Back

To write a linear equation given a slope (m) and a point (x1, y1), use the point-slope form: y - y1 = m(x - x1).

Front

What does it mean for a linear function to be increasing or decreasing?

Back

A linear function is increasing if its slope is positive (m > 0) and decreasing if its slope is negative (m < 0).

Front

How do you determine if a linear equation is in standard form?

Back

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