Writing Linear Equations From A Graph

Front

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

Back

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

Front

How do you identify the slope from a graph?

Back

The slope is the ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What does the y-intercept represent 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.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, the value of y increases by 2 units.

Front

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

Back

Use the formula for slope (m = (y2 - y1) / (x2 - x1)) to find the slope, then use the point-slope form to write the equation.

Front

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

Back

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

Front

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

Back

Rearrange the equation y - y1 = m(x - x1) to solve for y, resulting in y = mx + b.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

How can you determine if a line is horizontal or vertical from a graph?

Back

A horizontal line has a slope of 0 and is represented by y = b. A vertical line has an undefined slope and is represented by x = a.

Front

What does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts, meaning they will never intersect.