Slope Intercept 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 identify the slope in the equation y = -x + 3?

Back

In the equation y = -x + 3, the slope (m) is -1.

Front

What does the y-intercept represent in the equation y = 3x + 4?

Back

In the equation y = 3x + 4, the y-intercept (b) is 4, which means the line crosses the y-axis at the point (0, 4).

Front

How can you convert the equation y = 4/3x + 3 into standard form?

Back

To convert y = 4/3x + 3 into standard form, multiply through by 3 to eliminate the fraction: 3y = 4x + 9, then rearrange to 4x - 3y + 9 = 0.

Front

What is the slope of the line represented by the equation y = 2/3x - 1?

Back

The slope of the line represented by the equation y = 2/3x - 1 is 2/3.

Front

How do you find the x-intercept of the equation y = -1/3x - 2?

Back

To find the x-intercept of the equation y = -1/3x - 2, set y to 0 and solve for x: 0 = -1/3x - 2, which gives x = -6.

Front

What is the significance of the slope in a linear equation?

Back

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

Front

How can you graph the equation y = -x + 3?

Back

To graph y = -x + 3, start at the y-intercept (0, 3) and use the slope of -1 to find another point: from (0, 3), go down 1 unit and right 1 unit to (1, 2).

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship between the two variables.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.