Question

(3,10) and (6,12) put in slope intercept form

Answer 1

the slope-intercept form is:

$y=mx+b$

Where m is the slope

b is the y-intercept

The rule to find the slope is:

$m=\frac{y_2-y_1}{x_2-x_1}$

The points (3, 10) and (6, 12) are on the line, so let us use them

x1 = 3, x2 = 6

y1 = 10, y2 = 12

let us substitute them in the rule of m

$m=\frac{12-10}{6-3}=\frac{2}{3}$

Substitute m in the form of the equation

$y=\frac{2}{3}x+b$

To find b substitute x and y by the coordinates of any given point

let x = 3 and y = 10 (1st point)

$\begin{gathered} 10=\frac{2}{3}(3)+b \\ 10=2+b \\ 10-2=2-2+b \\ 8=b \end{gathered}$

The value of b is 8, substitute it in the equation

$y=\frac{2}{3}x+8$

This is the slope-intercept form of the line passes through the given points