Questions: (A) Find the slope of the line that passes through the given points. (B) Find the standard form of the equation of the line. (C) Find the slope-intercept form of the equation of the line. (4,6) and (11,11)

Solution Steps

To find the slope of the line passing through the points \((4, 6)\) and \((11, 11)\), we use the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the given values, we get \(m = \frac{11 - 6}{11 - 4} = 0.71\).

Using the point-slope form \(y - y_1 = m(x - x_1)\) with \(m = 0.71\), \(x_1 = 4\), and \(y_1 = 6\), we get the equation \(y - 6 = 0.71(x - 4)\).

From the point-slope form, we can derive the slope-intercept form \(y = mx + b\). Substituting \(m = 0.71\) and solving for \(b\), we get \(b = 3.14\). Therefore, the slope-intercept form is \(y = 0.71x + 3.14\).

Rearranging the slope-intercept form into standard form \(Ax + By = C\), we get \(-0.71x + y = 3.14\).

Final Answer: