Equations from two points

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

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

Back

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

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept in the equation y = mx + b?

Back

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

Front

Given the points (2, 3) and (4, 7), what is the slope of the line?

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

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

Back

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

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you convert the slope-intercept form to standard form?

Back

To convert y = mx + b to standard form, rearrange it to Ax + By = C by moving mx to the left side.

Front

What is the slope of the line represented by the equation 2x + 3y = 6?

Back

To find the slope, rewrite in slope-intercept form: 3y = -2x + 6, so y = -\frac{2}{3}x + 2. The slope is -\frac{2}{3}.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.