Checkpoint 5B: 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) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

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 an equation of a line written as 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 (0, b) in a linear equation?

Back

The coordinates (0, b) represent the y-intercept of the line, where the line crosses the y-axis.

Front

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

Back

To determine if a point (x, y) lies on the line, substitute the x-value into the equation and see if the resulting y-value matches the y-coordinate of the point.

Front

What is the equation of the line that passes through (1, 2) and (3, 6)?

Back

The slope is (6 - 2) / (3 - 1) = 2. Using point-slope form: y - 2 = 2(x - 1) simplifies to y = 2x.