Question

3. Write an equation of a line with a slope of 3. 4. Write the same equation from #3, but in a different way 5. What is the coordinate point of the y intercept of the line y = -3x + 7?

Answer 1

Question 3:

The equation of a line may be written in many forms.

One of them is the slope-intercept form.

The slope-intercept form is given by

`y=mx+b`

Where m is the slope and b is the y-intercept of the line.

For question 3,

We have slope m = 3

Since y-intercept is not given we can consider it zero (b = 0)

So the equation of the line may be written as

`y=3x`

Question 4:

Another way to write the equation of a line is called the point-slope form.

The point-slope form is given by

`(y-y_1)=m(x-x_1)`

Where (x₁, y₁) is a point on the line and m is the slope.

`(y-y_1)=3(x-x_1)`

If you substitute any point on this line into the above equation and simplify it then you will always end up with the same equation as before.

For example:

In the previous problem, we found that (1, 3) is a point on the line having the slope m = 3

`(y-3)=3(x-1)`

Let us simplify it

`\begin{gathered} y-3=3x-3 \\ y=3x-3+3 \\ y=3x \end{gathered}`

Hence, we got the same equation as in question 3

Answer to question 3:

`y=3x`

Answer to question 4:

`(y-y_1)=3(x-x_1)`