Writing Equations from a point and slope

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 write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), substituting the slope (m) and the coordinates of the point (x1, y1).

Front

What is 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

Write the equation of the line with slope -2 through the point (7, −1).

Back

y = -2x + 13.

Front

Which equation represents a line with a slope of 3 passing through (0, 9)?

Back

y = 3x + 9.

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

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

Back

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

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

Write the point-slope form of the equation of the line through (4, 1) with slope -1.

Back

y - 1 = -(x - 4).

Front

Write the equation in point-slope form of the line that passes through (4, -7) with slope -1/4.

Back

y + 7 = -1/4(x - 4).