Linear Equation from 2 points

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 does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive or negative).

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

Front

How can you determine the equation of a line given two points?

Back

1. Calculate the slope using the two points. 2. Use one of the points and the slope to solve for the y-intercept. 3. Write the equation in the form y = mx + b.

Front

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

Back

y = 2x - 2.

Front

What is the equation of the line that passes through the points (-2, 4) and (1, 10)?

Back

y = -2x + 8.

Front

How do you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x and y values. If the differences in y-values divided by the differences in x-values are constant, it is linear.

Front

What is the equation of the linear function that has a slope of 3 and a y-intercept of 6?

Back

y = 3x + 6.

Front

What does it mean for a line to be increasing?

Back

A line is increasing if the slope is positive, meaning as x increases, y also increases.