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 y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Front

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

Back

To convert from slope-intercept form (y = mx + b) to point-slope form (y - y1 = m(x - x1)), identify a point (x1, y1) on the line and use the slope m.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

Front

Given the point (4, 0) and slope m = 7, write the equation in point-slope form.

Back

y - 0 = 7(x - 4).

Front

For the equation y + 1 = -3(x - 5), what is the slope?

Back

The slope is -3.

Front

What is the point given in the equation y - 2 = 3(x + 1)?

Back

The point is (-1, 2).

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

Write the point-slope form for a line with slope -2/3 and passing through the point (0, -4).

Back

y + 4 = -2/3(x - 0).

Front

What is the y-intercept in the equation y = mx + b?

Back

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

Front

How do you determine if a point lies on a line given by an equation?

Back

Substitute the x and y coordinates of the point into the equation. If the equation holds true, the point lies on the line.