Question

What is the y-intercept of a line that passes through the points (2, 7) and (6, 1

Answer 1

To find the y-intercept of the line, we must find the equation of the line

The form of the linear equation is

$y=mx+b$

m is the slope

b is the y-intercept

The rule of the slope is

$m=\frac{y2-y1}{x2-x1}$

Where (x1, y1) and (x2, y2) are two points on the line

Since the line passes through points (2, 7) and (6, 1), then

x1 = 2 and y1 = 7

x2 = 6 and y2 = 1

Substitute them in the rule above

$m=\frac{1-7}{6-2}=\frac{-6}{4}=-\frac{3}{2}$

Now put it in the form of the equation above

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

Now to find b substitute x and y in the equation by the coordinates of one of the 2 given point

Let us use point (2, 7)

x = 2 and y = 7

$\begin{gathered} 7=-\frac{3}{2}(2)+b \\ 7=-3+b \end{gathered}$

Add both sides by 3 to find b

$\begin{gathered} 7+3=-3+3+b \\ 10=b \end{gathered}$

B is the y-intercept, then

The y-intercept of the line is (0, 10)