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

Write the point-slope form of the line that passes through the point (-2, -1) with a slope of -3.

Back

y + 1 = -3(x + 2)

Front

If a line has a slope of 3 and passes through the point (1, 7), what is its equation in point-slope form?

Back

y - 7 = 3(x - 1)

Front

What does the slope (m) represent in the point-slope form of a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

To convert, solve for y: y - y₁ = m(x - x₁) becomes y = mx - mx₁ + y₁.

Front

What is the slope of the line represented by the equation y - 4 = 5(x - 2)?

Back

The slope is 5.

Front

Graph the line represented by the equation y + 2 = -3(x + 1). What is the slope and y-intercept?

Back

The slope is -3 and the y-intercept is -5.

Front

If a line passes through the point (2, 4) and has a slope of 5, what is the point-slope form of the equation?

Back

y - 4 = 5(x - 2)

Front

What is the y-intercept of the line given by the equation y - 7 = 3(x - 1)?

Back

The y-intercept is 4.

Front

How do you identify a point on a line given in point-slope form?

Back

You can identify a point by substituting a value for x into the equation and solving for y.