Question

Write the equation for the line in slope-intercept form.

Answer 1

y = 4x + 3

Explanation:

We are given the line shown in your question.

We want to write the equation of this line in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept

As we are given the graph of the line, we can pick any 2 points to help us find the equation; in this case, let's take (0,3) and (-1, -1).

First, we need to find the slope of the line

The slope (m) can be found using the equation
`(y_2-y_1)/(x_2-x_1)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are points

Let's label the values of the points to avoid confusion and mistakes before calculating.

`x_1= 0\\y_1=3\\x_2=-1\\y_2=-1`

Now substitute these values into the equation for the slope

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

m=
`(-1-3)/(-1-0)`

Subtract

m=
`(-4)/(-1)`

Divide

m = 4

The slope of the line is 4

Here is the equation of the line so far:

y = 4x + b

Now we need to find b

As stated above, b is the value of y at the y intercept; the y intercept is the point where the line intersects with the y axis. The value of x at this point is 0

One of the points we used to calculate the slope was actually the y intercept point; this point is (0, 3). The value of y at this point is 3, so the value of b is 3

Substitute 3 as b in our equation

y = 4x + 3

Topic: finding the equation of the line