Linear Equation Word Problems (point slope, standard)

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing a linear equation as y = mx + b, where m is the slope and b is the y-intercept.

Front

What is point-slope form?

Back

Point-slope form is a way of writing a linear equation using a point (x1, y1) on the line and the slope m, expressed as y - y1 = m(x - x1).

Front

What is standard form of a linear equation?

Back

Standard form is a way of writing a linear equation as Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How do you find the slope from two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does the slope represent in a linear equation?

Back

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

Front

How do you convert from point-slope form 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.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the slope-intercept form y = mx + b.

Front

How do you write an equation from a word problem?

Back

Identify the variables, determine the relationship between them, and then express that relationship as a linear equation.

Front

What is the significance of the x-intercept?

Back

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