Question

Write an equation of the line that passes through the point and has the given slope. Use slope-intercept form. $$ (-1,5), m=\frac{2}{3} $$

Short answer

The equation of the line is \(y=\frac{2}{3}x + \frac{17}{3}\)

Step-by-step solution

Use the given point and slope

The equation of a line using slope-intercept form is \(y = mx + b\). We substitute the given point \((-1,5)\) into the equation and the given slope \(\frac{2}{3}\), which would give us \(5 = \frac{2}{3}*(-1) + b\).

Calculate the y-intercept

Then, we solve for \(b\) to determine the y-intercept. By simplifying the equation, we get \(b = 5 + \frac{2}{3}\) which equates to \(b=\frac{17}{3}\).

Construct the final equation

Finally, we put the calculated \(b\) and the given \(m\) back into the slope-intercept form to get the equation in the format \(y=mx+b\), which results into \(y = \frac{2}{3}x + \frac{17}{3}\).