Writing Linear equations given two points

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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 or negative).

Front

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

Back

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

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

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

Back

1. Find the slope using the two points. 2. Use one of the points and the slope to write the equation in point-slope form: y - y1 = m(x - x1). 3. Rearrange to slope-intercept form if needed.

Front

What is point-slope form of a linear equation?

Back

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

Front

Convert the point-slope form to slope-intercept form.

Back

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

Front

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

Back

The coordinates (x, y) represent points on the line. If a linear equation is true for a pair of coordinates, that point lies on the line.

Front

How do you determine if a point lies on a line represented by a linear equation?

Back

Substitute the x-coordinate of the point into the equation. If the resulting y-value matches the y-coordinate of the point, it lies on the line.

Front

What is the relationship between parallel lines in terms of slope?

Back

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