4.1: GRAPHING EQUATIONS IN SLOPE INTERCEPT FORM

Front

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

Back

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

Front

What does the slope (m) represent in the equation y = mx + b?

Back

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

Front

What does the y-intercept (b) represent in the equation y = mx + b?

Back

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

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

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

Back

The slope of the line is -2.

Front

What is the y-intercept of the line represented by the equation y = 4x - 5?

Back

The y-intercept of the line is -5.

Front

How do you graph the equation y = 3x + 1?

Back

Start at the y-intercept (0, 1) and use the slope (3) to rise 3 units and run 1 unit to the right.

Front

What is the graph of y = -x + 2?

Back

The graph is a straight line with a slope of -1 and a y-intercept at (0, 2).

Front

What is the equation of a line with a slope of 2 that passes through the point (1, 3)?

Back

Using the point-slope form, the equation is y - 3 = 2(x - 1), which simplifies to y = 2x + 1.

Front

How do you convert the equation y = 2x + 3 to standard form?

Back

To convert to standard form, rearrange to get -2x + y = 3 or 2x - y = -3.