HW/CW Linear Equations

Front

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

Back

The 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

How do you write the equation of a line in point-slope form given a point and a slope?

Back

To write the equation, use the formula y - y₁ = m(x - x₁) by substituting the given point (x₁, y₁) and the slope m.

Front

Calculate the slope between the points (3, 7) and (7, 2).

Back

The slope m is calculated as m = (y₂ - y₁) / (x₂ - x₁) = (2 - 7) / (7 - 3) = -5/4.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

If a line has a slope of -1/4, what does this indicate about its direction?

Back

A slope of -1/4 indicates that for every 4 units moved to the right, the line moves down 1 unit, showing a downward trend.

Front

What is the significance of the point (4, -7) in the context of linear equations?

Back

The point (4, -7) can be used as a reference point to write the equation of a line in point-slope form.

Front

How do you convert point-slope form to slope-intercept form?

Back

To convert, solve for y in the equation y - y₁ = m(x - x₁) to get y = mx + b.

Front

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

Back

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

Front

What is the y-intercept of the line represented by the equation y = -1/4(x - 4) + 7?

Back

To find the y-intercept, set x = 0 and solve for y. The y-intercept is 8.

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

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