Standard Form

Front

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

Back

The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y by isolating it on one side of the equation.

Front

What is the x-intercept of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept from the equation 3x + 8y = 24?

Back

To find the x-intercept, set y = 0 and solve for x: 3x + 8(0) = 24, which gives x = 8.

Front

What is the slope of the line represented by the equation 5x + 10y = 30?

Back

To find the slope, convert to slope-intercept form: 10y = -5x + 30, then y = -1/2x + 3, so the slope m = -1/2.

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; it indicates how steep the line is.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept from the equation 6x - 2y = 18?

Back

To find the y-intercept, set x = 0 and solve for y: 6(0) - 2y = 18, which gives y = -9.

Front

What is the relationship between the slope and the angle of a line?

Back

The slope of a line is equal to the tangent of the angle that the line makes with the positive x-axis.

Front

What is the significance of the coefficients in the standard form of a linear equation?

Back

In the standard form Ax + By = C, A and B determine the slope of the line, while C represents the point where the line intersects the axes.