Solving for b

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) between 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 slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

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

Back

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

Front

Write the equation of a line with slope m = -1 through the point (2, 3).

Back

y = -x + 5.

Front

Write the equation of a line with slope m = 5/4 through the point (-4, -3).

Back

y = 5/4x + 2.

Front

Write the slope-intercept form of the equation through (-1, 4) with m = -3.

Back

y = -3x + 1.

Front

Write the equation of a line with slope m = -2 through the point (3, -1).

Back

y = -2x + 5.

Front

How do you determine if a line is increasing or decreasing based on its slope?

Back

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

Front

What is the formula to convert a point-slope equation to slope-intercept form?

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + (y1 - mx1).