Writing 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

Write the equation of a line with a slope of -2 and a y-intercept of 4.

Back

y = -2x + 4.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = a, where a is the x-coordinate of any point on the line.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = b, where b is the y-coordinate of any point on the line.

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/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

Write the equation of a line that passes through the points (1, 2) and (3, 6).

Back

First, find the slope: m = (6-2)/(3-1) = 2. Then use point-slope form: y - 2 = 2(x - 1) leads to y = 2x.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, where all points have the same x-coordinate.