Slope-Intercept Form of an Equation

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 find the slope (m) from 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 y-intercept (b) represent in the slope-intercept form?

Back

The y-intercept b is the point where the line crosses the y-axis, represented as (0, b).

Front

Write the equation of the line in slope-intercept form with slope m = 4 through the point (0, 5).

Back

y = 4x + 5.

Front

Graph the line with the equation y = -\frac{1}{3}x - 4. What is the slope and y-intercept?

Back

The slope is -\frac{1}{3} and the y-intercept is -4.

Front

Write the equation of the line in slope-intercept form through the points (2, 5) and (4, 9).

Back

y = 2x + 1.

Front

What is the slope of the line represented by the equation y = (-3/2)x + 4?

Back

The slope is -\frac{3}{2}.

Front

If a line has a slope of 4, what does this indicate about the line's steepness?

Back

A slope of 4 indicates that for every 1 unit increase in x, y increases by 4 units, making the line steep.

Front

Write the equation of the line in slope-intercept form of the table where the slope is 4 and the y-intercept is 6.

Back

y = 4x + 6.

Front

What is the significance of the slope in a real-world context?

Back

The slope represents the rate of change between two variables, such as speed or cost per item.