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 find the slope 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 slope represent in a linear equation?

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 slope-intercept form?

Back

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

Front

Convert the equation 5x - 3y = -9 to slope-intercept form.

Back

y = (5/3)x + 3.

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 a line with slope m = -2 that passes through the point (3, 1).

Back

y = -2x + 7.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does a negative slope indicate about the direction of a line?

Back

A negative slope indicates that as x increases, y decreases, resulting in a line that slopes downward.

Front

How do you graph a line using the slope-intercept form?

Back

Start by plotting the y-intercept (b) on the y-axis, then use the slope (m) to find another point by rising and running.