Forms of Linear Equations

Front

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

Back

The point-slope form of a linear equation is given by 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 y-intercept of a linear equation in standard form?

Back

To find the y-intercept of a linear equation in standard form (Ax + By = C), set x = 0 and solve for y.

Front

What is the slope of a line in the equation y + 1 = -3(x - 5)?

Back

The slope of the line is -3.

Front

How do you determine the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.

Front

What are the x and y intercepts of the equation 4x - 5y = 40?

Back

The x-intercept is 10 and the y-intercept is -8.

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, indicating how steep the line is.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers and A ≥ 0.

Front

How can you convert the point-slope form to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of the y-intercept in a graph?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope but different y-intercepts.