Question

Find the equation of the line passingthrough the points (3, 3) and (4, 5).y = [? ]x + [AEnter

Answer 1

y = 2x - 3

Step-by-step explanation:

The slope-intercept form of the equation of a line is generally given as;

`y=mx+b`

where m = the slope of the line

b = the y-intercept of the line

The slope(m) of the line can be determined using the below formula;

`m=(y_2-y_1)/(x_2-x_1)`

Given the points (3, 3) and (4, 5), so our x1 = 3, x2 = 4, y1 = 3, and y2 = 5.

Let's substitute these values into our slope formula and solve for m;

`m=(5-3)/(4-3)=(2)/(1)=2`

Let's go ahead and use point (3, 3) where x = 3 and y = 3 with slope(m) = 2 to determine the y-intercept(b);

`\begin{gathered} y=mx+b \\ 3=2(3)+b \\ 3=6+b \\ b=3-6 \\ b=-3 \end{gathered}`

We now have m = 2 and b = -3, therefore the required equation of a line can be written as;

`y=2x-3`