Equation of a straight line

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 - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

Front

How do you calculate the slope (m) between two points (x_1, y_1) and (x_2, y_2)?

Back

The slope (m) is calculated using the formula: m = (y_2 - y_1) / (x_2 - x_1).

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

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

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 do you convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y_1 = m(x - x_1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is given by the formula: Ax + By = C, where A, B, and C are integers.

Front

How do you find the equation of a line given two points?

Back

1. Calculate the slope (m) using the two points. 2. Use one point and the slope to write the equation in point-slope form. 3. Convert to slope-intercept or standard form if needed.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope (m) but different y-intercepts.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other, meaning if one line has a slope of m, the other has a slope of -1/m.

Front

How do you determine if a point lies on a line given its equation?

Back

Substitute the x-coordinate of the point into the equation of the line and check if the resulting y-value matches the y-coordinate of the point.