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 slope from a graph?

Back

To find the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and then use the formula slope (m) = rise/run.

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 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 one of the points and the slope to write the equation in point-slope form: y - y1 = m(x - x1).

Front

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

Back

The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

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

Back

To convert 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 it mean if a line has a negative slope?

Back

If a line has a negative slope, it means that as x increases, y decreases. The line goes downwards from left to right.

Front

What does it mean if a line has a positive slope?

Back

If a line has a positive slope, it means that as x increases, y also increases. The line goes upwards from left to right.

Front

How can you determine if a linear equation is correct by looking at a graph?

Back

You can determine if a linear equation is correct by checking if the line represented by the equation passes through the points indicated on the graph.