Point-Slope, Slope Intercept, Standard Form

Front

What is the point-slope form of a linear equation?

Back

The point-slope form is given by the equation: y - y_1 = m(x - x_1), where (x_1, y_1) is a point on the line and m is the slope.

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 and the direction it goes (positive slope = rising, negative slope = falling).

Front

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

Back

To convert, solve for y: y - y_1 = m(x - x_1) becomes y = mx - mx_1 + y_1.

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 y-intercept from the slope-intercept form?

Back

The y-intercept is the value of y when x = 0, which is represented by b in the equation y = mx + b.

Front

What is the standard form of a linear equation?

Back

The standard form is given by the equation: Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you find the x-intercept from the standard form?

Back

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

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope. If two lines are parallel, their slopes (m) are equal.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope m, the other line's slope is -1/m.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

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