Flashcard Review - Point-Slope, Slope Intercept, Standard

The point-slope form is given by the equation: $$y - y_1 = m(x - x_1)$$ , where $$m$$ is the slope and $$(x_1, y_1)$$ is a point on the line.

The slope $$m$$ is calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

The slope-intercept form is given by the equation: $$y = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

The y-intercept is the value of $$y$$ when $$x = 0$$ ; it is the point where the line crosses the y-axis.

To convert, distribute and solve for $$y$$ : $$y = \frac{1}{4}x + \frac{5}{2}$$ .

The standard form is given by the equation: $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers.

Rearrange the equation $$y = mx + b$$ to the form $$Ax + By = C$$ by moving terms around.

The coefficients $$A$$ and $$B$$ indicate the direction and steepness of the line, while $$C$$ represents the line's position.

The equation is: $$y - 3 = 4(x - 2)$$ .