Writing Equations from Two Points

Front

What is the formula to find the slope (m) 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 in a graph?

Back

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

Front

What is the y-intercept in the equation of a line in the form y = mx + b?

Back

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

Front

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

Back

To convert y = mx + b to Ax + By = C, rearrange the equation to get all terms on one side.

Front

What is the slope of the line that passes through the points (2, 3) and (5, 9)?

Back

The slope is m = (9 - 3) / (5 - 2) = 6 / 3 = 2.

Front

Write the equation of the line in slope-intercept form that passes through (1, 2) with a slope of 3.

Back

The equation is y = 3x - 1.

Front

What is the slope of the line that passes through the points (4, 5) and (4, 1)?

Back

The slope is undefined because the x-coordinates are the same, indicating a vertical line.

Front

If a line has a slope of -2, what does this indicate about the direction of the line?

Back

A slope of -2 indicates that the line descends from left to right.

Front

How do you find the equation of a line given two points?

Back

First, calculate the slope using the two points, then use the point-slope form to write the equation.

Front

What is the point-slope form of a line's equation?

Back

The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line.