Explain Point [7.PR.2c]

Front

What does it mean for two quantities to be proportional?

Back

Two quantities are proportional if they maintain a constant ratio to each other, meaning as one quantity increases or decreases, the other does so in a consistent manner.

Front

How do you determine the rate of change from a point on a graph?

Back

The rate of change can be determined by finding the slope of the line, which is calculated as the change in the y-value divided by the change in the x-value between two points.

Front

What is the formula for calculating the slope of a line?

Back

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

Front

If a point (3, 180) is plotted on a graph representing distance and time, how can you find the speed?

Back

To find the speed, divide the distance (180 miles) by the time (3 hours), resulting in a speed of 60 miles per hour.

Front

What is the general form of a linear equation representing a proportional relationship?

Back

The general form is y = kx, where k is the constant of proportionality.

Front

How can you express a proportional relationship in terms of a graph?

Back

A proportional relationship is represented by a straight line that passes through the origin (0,0) on a graph.

Front

What does the constant of proportionality represent in a proportional relationship?

Back

The constant of proportionality (k) represents the factor by which one quantity changes in relation to another; it is the slope of the line in a graph.

Front

How do you write an equation from a graph that shows a proportional relationship?

Back

Identify the slope of the line and the y-intercept (which is 0 for proportional relationships), then use the slope to write the equation in the form y = kx.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0. In proportional relationships, the y-intercept is always 0.

Front

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

Back

First, calculate the slope using the two points, then use one of the points and the slope to write the equation in point-slope form, which can be converted to slope-intercept form.