Question

Find the equation of the line through the points (0, –3) and (4, 5)

Answer 1

Answer:

y=2x-3

Step-by-step explanation:

Hi there!

We are given the points  (0, –3) and (4, 5)

We want to find the equation of the line between these points

There are 3 ways to write the equation of the line, yet the most common way is slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

To write the equation of the line in this way, we need to first find the slope of the line
The slope can be found using the formula $\frac{y_2-y_1}{x_2-x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points

We already have 2 points, but let's label their values to avoid confusion and mistakes when calculating.

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

m=$\frac{5--3}{4-0}$

Simplify

m=$\frac{5+3}{4-0}$

m=$\frac{8}{4}$

Divide

m=2

We found the slope of the line.

Here is the equation of the line so far:

y=2x+b

Now let's find b

As stated before, b is the y intercept of the line, which is the point where the line passes through the y axis; the value of x at the y intercept is 0

One of the points we were given (0, -3) is actually the y intercept of the line!

The value of b is the value of y at the y intercept; in this case, b is equal to -3

Now substitute -3 as b in the equation.

y=2x-3

Hope this helps!

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