Question

Write the equation of each line in slope‐intercept form.

Answer 1

y = -x +4

Explanation:

Hi there!

We are given the equation of a line, and we want to write the equation of this line in slope-intercept form

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

First, we need to find the slope of the line

The slope (m) can be calculated from 2 points, using the formula
`(y_2-y_1)/(x_2-x_1)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are points

First, let's find 2 points on the line:

The intercepts - the points where the line hits the x and y axis are a good place to start; the intercepts of this line are (4,0) and (0, 4), which will also work for calculating the slope

Let's label the values of these 2 points to avoid any confusion and mistakes when calculating.

`x_1=4\\y_1=0\\x_2=0\\y_2=4`

Substitute into the formula

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

m=
`(4-0)/(0-4)`

Subtract

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

Divide

m = -1

The slope of the line is -1

We can substitute that into our equation:

y = -x + b (when -1 is the leading coefficient, only adding a minus sign in front of the variable will suffice)

Now we need to find b

As said earlier, b is the value of y at the y intercept

The point of the y intercept is (0, 4), and the value of y at this point is 4

So substitute 4 as b into the equation

y = -x + 4

Hope this helps!