Writing Equations of Lines

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

Back

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

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 b in the slope-intercept form y = mx + b.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates that the line is horizontal.

Front

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

Back

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Front

How can you determine if two lines are parallel?

Back

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

Front

What is the equation of a line with a slope of 2 and a y-intercept of -3?

Back

The equation is y = 2x - 3.

Front

How do you convert the standard form of a linear equation Ax + By = C to slope-intercept form?

Back

To convert, solve for y: y = (-A/B)x + (C/B).

Front

What is the slope of the line represented by the equation y = -4x + 7?

Back

The slope of the line is -4.

Front

What is the equation of a line that passes through the point (3, 2) with a slope of 1?

Back

The equation is y - 2 = 1(x - 3), which simplifies to y = x - 1.