Writing Equations in 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 of a line given 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 of a line?

Back

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

Front

Given a slope of 1/2 and a point (8,5), how do you write the equation in slope-intercept form?

Back

Using the point-slope form: y - 5 = (1/2)(x - 8) simplifies to y = (1/2)x + 1.

Front

What is the equation of a line with a slope of 6 that passes through the point (1,8)?

Back

Using the point-slope form: y - 8 = 6(x - 1) simplifies to y = 6x + 2.

Front

How do you convert the slope-intercept form to standard form?

Back

To convert y = mx + b to standard form Ax + By = C, rearrange the equation to get all terms on one side.

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent speed, growth rate, or any rate of change in various contexts.

Front

How do you determine the y-intercept from a linear equation in slope-intercept form?

Back

The y-intercept is the constant term (b) in the equation y = mx + b.

Front

Write the equation of a line with slope = 5 that goes through point (3, -5).

Back

Using point-slope form: y + 5 = 5(x - 3) simplifies to y = 5x - 20.