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 between 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 in the equation y = mx + b?

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

If a line has a slope of 1, what does that mean?

Back

A slope of 1 means that for every unit increase in x, y increases by the same amount; the line rises at a 45-degree angle.

Front

Write the equation of a line with a slope of 2 that passes through the point (3, 4).

Back

Using the point-slope form: y - 4 = 2(x - 3), the equation simplifies to y = 2x - 2.

Front

What is the slope of the line that passes through the points (1, 2) and (3, 6)?

Back

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

Front

How do you convert the equation 2x - 3y = 6 into slope-intercept form?

Back

Rearranging gives y = (2/3)x - 2; the slope is 2/3 and the y-intercept is -2.

Front

What is the significance of a negative slope?

Back

A negative slope indicates that as x increases, y decreases; the line falls from left to right.

Front

If a line is horizontal, what is its slope?

Back

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