Writing Equations in Point-Slope Form

Front

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

Back

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

Front

How do you find the slope between two points?

Back

The slope (m) between two points (x1, y1) and (x2, y2) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (-4, -6) and (3, 8)?

Back

The slope of the line is 2, calculated as m = (8 - (-6)) / (3 - (-4)) = 14 / 7 = 2.

Front

Given the point-slope equation y + 6 = 2(x + 4), what point does the line pass through?

Back

The line passes through the point (-4, -6).

Front

What is the significance of the point (x1, y1) in the point-slope form?

Back

The point (x1, y1) represents a specific point on the line, which is used to define the line's position.

Front

How do you convert a point-slope equation to slope-intercept form?

Back

To convert from point-slope form (y - y1 = m(x - x1)) to slope-intercept form (y = mx + b), solve for y.

Front

What is the equation of a line that goes through the points (-3, 9) and (0, 1)?

Back

The equation is y - 9 = -8/3(x + 3).

Front

What does the slope 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

If a line has a slope of 1/2, what does this mean in terms of rise over run?

Back

A slope of 1/2 means that for every 2 units you move horizontally (run), the line rises 1 unit (rise).

Front

What is the y-intercept of the line given by the equation y + 6 = 1/2(x + 2)?

Back

The y-intercept is -6, which is the value of y when x = 0.