Writing a Linear Equation from a Table or Two Points

Front

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

Back

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

Front

How do you calculate the y-intercept of a line given a point and the slope?

Back

To calculate the y-intercept (b), use the formula b = y - mx, where (x, y) is the point on the line and m is the slope.

Front

What is the slope of a line that passes through the points (2, 2) and (3, 4)?

Back

The slope (m) is calculated as (y2 - y1) / (x2 - x1) = (4 - 2) / (3 - 2) = 2.

Front

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

Back

To write the equation of a line given two points, first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1), then use the point-slope form y - y1 = m(x - x1) to find the equation.

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept represents the point where the line crosses the y-axis, indicating the value of y when x = 0.

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 much y increases or decreases for a unit increase in x.

Front

How can you determine if an equation matches a given table of values?

Back

To determine if an equation matches a table of values, substitute the x-values from the table into the equation and check if the resulting y-values match those in the table.

Front

What is the equation of a line with a slope of 4 and a y-intercept of 6?

Back

The equation of the line is y = 4x + 6.

Front

How do you convert a point-slope equation to slope-intercept form?

Back

To convert a point-slope equation (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

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