Writing Linear Equations from a graph

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 y-intercept from a graph?

Back

The y-intercept is the point where the line crosses the y-axis. It can be found by looking at the value of y when x = 0.

Front

What is the formula for slope?

Back

The formula for slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Front

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

Back

The y-intercept represents the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How can you write the equation of a line given the slope and y-intercept?

Back

You can write the equation in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases. The line goes downwards from left to right.

Front

What does it mean if a line is horizontal?

Back

A horizontal line has a slope of 0, meaning there is no change in y as x changes. The equation is of the form y = b.

Front

What does it mean if a line is vertical?

Back

A vertical line has an undefined slope, meaning x is constant and does not change. The equation is of the form x = a.

Front

How do you determine the slope from a graph?

Back

To determine the slope from a graph, pick two points on the line, find the rise (change in y) and run (change in x), and use the slope formula.