Solving & Graphing Slope-Intercept Form

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 calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

If a line has a slope of -2/3, what does this indicate about its direction?

Back

A slope of -2/3 indicates that the line descends from left to right.

Front

What is the slope of the line that passes through the points (0, -2) and (3, -4)?

Back

The slope is -2/3.

Front

How do you convert the equation -6x + 3y = 9 into slope-intercept form?

Back

Rearranging gives y = 2x + 3.

Front

What does the equation y = 3x represent graphically?

Back

It represents a line with a slope of 3 that passes through the origin (0,0).

Front

What is the significance of the equation x = -5?

Back

This equation represents a vertical line that crosses the x-axis at -5.

Front

How can you identify the graph of the equation y = -3x + 4?

Back

The graph will have a slope of -3 and a y-intercept at (0, 4).