Question

Write an equation of the line passing through each of the following pairs of points.

Answer 1

Answer:

y = $\frac{3}{4}$ x

Step-by-step explanation:

The equation of a line passing through the origin (0, 0 ) is

y = mx ( where m is the slope )

m = $\frac{rise}{run}$ = $\frac{3}{4}$, thus

y = $\frac{3}{4}$ x

Answer 2

Answer:

The equation of the line passing through (0,0) and (4,3) is  $y=\frac{3}{4} x$

Solution:

Given pair of points are (0,0) and (4,3)

Here, $x_{1}=0 ; y_{1}=0 ; x_{2}=4 ; y_{2}=3$

We know the slope of an equation is given by y = mx+c

Where “m” is the slope of the line and “c” is the y-intercept

To find the value of m, we use the below given formula

$\mathrm{m}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Substituting the values we get,

$\mathrm{m}=\frac{3-0}{4-0}=\frac{3}{4}$

Putting the value of m in the slope intercept form we get,

$y=\frac{3}{4}x + c$

To find the value of c, we substitute the value of x and y from any two given point. Lets take x = 4 and y = 3

$\begin{array}{l}{3=\frac{3}{4}(4)+c} \\ {3=3+c} \\ {c=0}\end{array}$

Therefore the slope intercept equation becomes $y=\frac{3}{4} x$