Writing Equations of Lines from Tables, Graphs, and 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 find the slope from 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 a y-intercept?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Write the equation of a line with a slope of 2 and a y-intercept of 5 in slope-intercept form.

Back

y = 2x + 5.

Front

If a line has a slope of -1, what does this indicate about the line's direction?

Back

A slope of -1 indicates that the line descends from left to right.

Front

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

Back

y - 2 = 3(x - 1) or y = 3x - 1.

Front

How can you determine the equation of a line from a table of values?

Back

Identify the slope by calculating the change in y over the change in x, then use a point from the table to write the equation.

Front

What is the significance of the equation y = 4x + 3?

Back

This equation indicates a line with a slope of 4 and a y-intercept of 3.

Front

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

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + b.