Linear Equations

Front

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

Back

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

Front

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

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y to isolate it on one side.

Front

What does the slope of a line represent in a real-world context?

Back

The slope represents the rate of change of the dependent variable with respect to the independent variable, indicating how much y changes for a unit change in x.

Front

What is the y-intercept of a linear equation?

Back

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

Front

How can you determine the initial value in a linear equation from a word problem?

Back

The initial value can often be found by identifying the value of the dependent variable when the independent variable is zero.

Front

What is point-slope form of a linear equation?

Back

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

Front

How do you find the equation of a line given a point and a slope?

Back

Use the point-slope form of the equation: y - y1 = m(x - x1), substituting the given point (x1, y1) and the slope m.

Front

What is the significance of the coefficients in a linear equation?

Back

The coefficients indicate the slope and the y-intercept, which determine the steepness and position of the line on the graph.

Front

How do you interpret the slope in a real-world scenario?

Back

The slope can indicate speed, growth rate, or any other rate of change relevant to the context of the problem.

Front

What is the relationship between two variables in a linear equation?

Back

In a linear equation, there is a constant rate of change between the two variables, meaning that as one variable increases or decreases, the other does so in a predictable manner.