Slope Intercept Form

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 find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How can you convert a point-slope form equation to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of the slope in the equation y = mx + b?

Back

The slope (m) 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 write the equation of a line given a point and a slope?

Back

Use the point-slope form: y - y1 = m(x - x1), then rearrange to slope-intercept form if needed.

Front

What is the formula to find the y-intercept when given a slope and a point?

Back

Use the formula b = y - mx, where (x, y) is the point and m is the slope.

Front

How do you determine if two lines are parallel using their slopes?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other; if one slope is m, the other is -1/m.