Writing Linear Equations

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 find the slope (m) from two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept (b) represent in a linear equation?

Back

The y-intercept b is the value of y when x = 0; it represents the point where the line crosses the y-axis.

Front

Given the points (-4,-2) and (-3,5), what is the slope of the line connecting them?

Back

The slope m = (5 - (-2)) / (-3 - (-4)) = 7.

Front

Write the equation in slope-intercept form for the line with slope 7 and y-intercept 26.

Back

The equation is y = 7x + 26.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

Front

How do you convert the equation y - 80 = 40(x - 2) into slope-intercept form?

Back

Distributing gives y - 80 = 40x - 80, so y = 40x.

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

If a linear equation is given as y = 3x + 1, what is the slope and y-intercept?

Back

The slope is 3 and the y-intercept is 1.

Front

How can you determine if a linear equation is increasing or decreasing?

Back

If the slope (m) is positive, the line is increasing; if the slope is negative, the line is decreasing.