Point slope Form

Front

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

Back

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

Front

How do you convert a linear equation from slope-intercept form to point-slope form?

Back

To convert from slope-intercept form (y = mx + b) to point-slope form (y - y₁ = m(x - x₁)), identify a point (x₁, y₁) on the line and use the slope m.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is and the direction it goes (positive or negative).

Front

Given the point (2, 3) and slope m = 4, write the equation in point-slope form.

Back

y - 3 = 4(x - 2)

Front

What is the significance of the point (x₁, y₁) in the point-slope form?

Back

The point (x₁, y₁) is a specific point on the line, which is used as a reference to write the equation in point-slope form.

Front

If a line has a slope of -2 and passes through the point (1, 5), what is the point-slope form of the equation?

Back

y - 5 = -2(x - 1)

Front

How can you determine the slope from a point-slope equation?

Back

The slope can be directly identified from the point-slope equation in the form y - y₁ = m(x - x₁), where m is the slope.

Front

What is the relationship between point-slope form and slope-intercept form?

Back

Point-slope form can be converted to slope-intercept form (y = mx + b) by simplifying the equation.

Front

Write the point-slope form of the line that passes through (0, 0) with a slope of 3.

Back

y - 0 = 3(x - 0) or y = 3x.

Front

For the equation y + 2 = 5(x - 1), what is the slope?

Back

The slope is 5.