Point-Slope to Slope-Intercept Form

Front

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

Back

The point-slope form is given by the equation: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert, solve for y in the point-slope equation: y - y1 = m(x - x1) to get y = mx + (y1 + m*x1).

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; it indicates how steep the line is.

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 y-intercept from a slope-intercept equation?

Back

The y-intercept is the value of y when x = 0, represented by b in the equation y = mx + b.

Front

Convert the equation y - 5 = 3(x + 2) to slope-intercept form.

Back

y = 3x + 11.

Front

What is the first step to convert y - 3 = -2(x + 4) to slope-intercept form?

Back

Distribute -2 to both terms in the parentheses: y - 3 = -2x - 8.

Front

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

Back

y - 3 = 4(x - 2).

Front

What is the significance of the coordinates in point-slope form?

Back

The coordinates (x1, y1) represent a specific point on the line, which is essential for defining the line's position.

Front

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

Back

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