Writing Equations in Slope-Intercept Form

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 find the slope (m) between two points (x1, y1) and (x2, y2)?

Back

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

Front

What does the y-intercept (b) represent in the slope-intercept form?

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 points (6,3) and (4,1), what is the slope of the line?

Back

The slope m = (1 - 3) / (4 - 6) = 2.

Front

Write the equation of the line in slope-intercept form that passes through (6,3) with a slope of 2.

Back

y = 2x - 9.

Front

What is the formula to convert a point-slope equation to slope-intercept form?

Back

Start with y - y1 = m(x - x1) and solve for y to get y = mx + (y1 - mx1).

Front

How do you determine the rate of change from a word problem involving distance and cost?

Back

The rate of change is found by dividing the change in cost by the change in distance.

Front

If a line has a slope of -6 and passes through the point (-3, 5), what is the equation in slope-intercept form?

Back

y = -6x - 13.

Front

What is the significance of a positive slope in a linear equation?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, meaning y remains constant regardless of x.