Point-Slope Form

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 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 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

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

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

Back

To convert, solve for y: y = mx + (y₁ - mx₁).

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

If a line has a slope of 3, what does this mean?

Back

It means that for every 1 unit increase in x, y increases by 3 units.

Front

Write the equation of a line with a slope of -2 that passes through the point (4, 5).

Back

Using point-slope form: y - 5 = -2(x - 4) simplifies to y = -2x + 13.

Front

What is the y-intercept of the line y = 4x + 1?

Back

The y-intercept is 1, which is the value of y when x = 0.