Writing Linear Equations Recap

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 (m) between 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 y-intercept (b) represent in the slope-intercept form?

Back

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

Front

How can you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y to isolate it on one side of the equation.

Front

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

Back

The slope indicates the rate of change of y with respect to x; a positive slope means the line rises, while a negative slope means it falls.

Front

Given the points (2, 3) and (4, 7), what is the slope of the line connecting them?

Back

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

Front

How do you determine the equation of a line given its slope and a point on the line?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the formula for finding the y-intercept from a linear equation in standard form?

Back

To find the y-intercept from Ax + By = C, set x = 0 and solve for y.

Front

How can you identify the slope and y-intercept from the equation y = 3x + 5?

Back

The slope (m) is 3 and the y-intercept (b) is 5.

Front

What is the relationship between the slopes of parallel and perpendicular lines?

Back

Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.