Writing Equations and Converting to Slope-Intercept

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you isolate y in the equation 2x + 4y = 8?

Back

Subtract 2x from both sides to get 4y = -2x + 8, then divide each term by 4 to solve for y.

Front

What does the slope (m) represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

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

Back

The y-intercept is the value of y when x = 0, representing where the line crosses the y-axis.

Front

Convert the equation y - 3 = -2(x + 4) to slope-intercept form.

Back

y = -2x - 5.

Front

What is the first step to convert 2x + 4y = 8 into slope-intercept form?

Back

Subtract 2x from both sides.

Front

If a line has a slope of 7, what does this indicate about the line's steepness?

Back

A slope of 7 indicates that for every 1 unit increase in x, y increases by 7 units, making the line steep.

Front

What is the significance of the point (4, -8) in the equation y + 8 = 7(x - 4)?

Back

It is a point on the line represented by the equation, confirming that the line passes through this coordinate.

Front

How do you find the slope from two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).

Front

What does it mean if two lines are parallel in terms of their slopes?

Back

Two lines are parallel if they have the same slope but different y-intercepts.