Writing Equations in Slope Intercept Form

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

The slope is calculated using the formula: $$m = \frac{y2 - y1}{x2 - x1}$$ .

The y-intercept is the point where the line crosses the y-axis, represented by the value of $$b$$ in the slope-intercept form $$y = mx + b$$ .

Using the slope formula, $$m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2$$ .

A slope of 0 indicates that the line is horizontal.

Using the point-slope form, the equation is: $$y - 2 = 3(x - 1)$$ , which simplifies to $$y = 3x - 1$$ .

To convert to standard form, rearrange to: $$2x - y = -5$$ .

A negative slope indicates that as x increases, y decreases, resulting in a downward slant of the line.

Using point-slope form: $$y - 4 = -1(x - 3)$$ , which simplifies to $$y = -x + 7$$ .

The slope of the line is -2.