Linear Equations From Tables & Graphs, 8.5I

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 linear equation represent?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the slope from a table of values?

Back

To find the slope from a table, calculate the change in y (rise) divided by the change in x (run) between two points: slope = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept of the equation y = 15x + 40 represent?

Back

The y-intercept is 40, which represents the flat fee charged by the hair stylist.

Front

What does the slope of the equation y = 0.5x + 10 represent?

Back

The slope is 0.5, which represents the per-mile fee for renting the moving truck.

Front

How can you identify the equation of a line from a graph?

Back

You can identify the equation by determining the slope and the y-intercept from the graph.

Front

What is the equation of a line with a slope of -3 and a y-intercept of -3?

Back

The equation is y = -3x - 3.

Front

What is the equation of a line with a slope of 1 and a y-intercept of -4?

Back

The equation is y = x - 4.

Front

How do you determine the y-intercept from the equation y = 2x + 5?

Back

The y-intercept is 5, which is the constant term in the equation.