Writing Linear Equations

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you determine the slope from 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 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 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, solve for y: y = (-A/B)x + (C/B).

Front

What is point-slope form of a linear equation?

Back

Point-slope form 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 write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the slope (m) and the coordinates of the point (x1, y1).

Front

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

Back

The slope indicates the steepness of the line and the direction of the relationship between x and y; a positive slope means the line rises, while a negative slope means it falls.

Front

How do you graph a linear equation in slope-intercept form?

Back

Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to determine the rise over run to plot additional points.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation represents a straight line, while a linear inequality represents a region of the graph that satisfies the inequality, often shaded.

Front

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

Back

First, calculate the slope using the two points, then use one of the points and the slope to write the equation in point-slope form.