Question

What is the slope intercept form of (3,1) and (9,-7)

Answer 1

The slope-intercept form of a line is given by:

$y=mx+b$

Where

• m is the slope of the line.

,

• b is the y-intercept of the line. At this point, x = 0.

Since we have two points: (3, 1) and (9, -7), we can use the two-points form of the line equation as follows:

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Now, we can label both points as follows:

• (3, 1) ---> x1 = 3, y1 = 1

,

• (9, -7) ---> x2 = 9, y2 = -7

If we apply the two-points form of the line equation, we have:

$\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-1=\frac{-7-1}{9-3}(x-3) \\ y-1=\frac{-8}{6}(x-3) \\ y-1=-\frac{4}{3}(x-3) \\ y-1=(-\frac{4}{3})(x)+(-\frac{4}{3})(-3) \\ y-1=-\frac{4}{3}x+4(-\frac{3}{-3}) \\ y-1=-\frac{4}{3}x+4(1) \\ y-1=-\frac{4}{3}x+4 \end{gathered}$

If we add 1 to both sides of the equation, we finally have:

$\begin{gathered} y-1+1=-\frac{4}{3}x+4+1 \\ y=-\frac{4}{3}x+5 \end{gathered}$

In summary, therefore, the slope-intercept form of the line that passes through the points (3, 1) and (9, -7) is:

$y=-\frac{4}{3}x+5$