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

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

Back

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

Front

What does the y-intercept (b) represent in a linear equation?

Back

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

Front

How do you find the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), then rearrange to slope-intercept form.

Front

If a line has a slope of 4 and passes through the point (-2, 5), what is the equation in slope-intercept form?

Back

y = 4x + 13.

Front

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

Back

Subtract 2x from both sides to isolate the 4y term.

Front

What is the final step to solve for y in the equation 4y = -2x + 8?

Back

Divide each term by 4.

Front

In the equation y = 3x + 8, what does the 3 represent?

Back

The 3 represents the slope of the line, indicating that for every 1 unit increase in x, y increases by 3 units.

Front

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

Back

The y-intercept can represent the starting value in a situation, such as initial quantity or cost.

Front

How can you determine if two lines are parallel using their equations?

Back

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