Graphing Linear Equations

Front

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

Back

The point-slope form of a linear equation is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you identify the slope and y-intercept from the equation y = mx + b?

Back

In the equation y = mx + b, m represents the slope of the line, and b represents the y-intercept, which is the point where the line crosses the y-axis.

Front

What does the slope of a line represent?

Back

The slope of a line 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 means the line rises, negative slope means it falls).

Front

What is the y-intercept of a line?

Back

The y-intercept of a line is the point where the line crosses the y-axis, represented by the coordinate (0, b) in the equation y = mx + b.

Front

How do you convert the equation y - y1 = m(x - x1) to slope-intercept form?

Back

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

Front

What is the significance of the coordinates (x1, y1) in the point-slope form?

Back

The coordinates (x1, y1) represent a specific point on the line, which is used to define the line's equation in point-slope form.

Front

How can you find the equation of a line given a slope and a point?

Back

To find the equation of a line given a slope (m) and a point (x1, y1), use the point-slope form: y - y1 = m(x - x1).

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is equal to the tangent of the angle (θ) that the line makes with the positive x-axis: m = tan(θ).

Front

How do you determine if two lines are parallel?

Back

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

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1 (m1 * m2 = -1).