Question

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

(Use integers or fractions for any numbers in the equation.)

Answer 1

y = 4x + 5

Explanation:

First, let's establish that the equation for slope-intercept form is:

y = mx + b where m is the line's slope and b is its y-intercept (where the line touches the y-axis or x = 0)

Next, find the line's slope using the formula:

`m=(y_2-y_1)/(x_2-x_1)` where the line goes through points
`(x_1,y_1)` and
`(x_2, y_2)`

To do this, we need to identify points on the line.

We'll use these two:

(0, 5) and (1, 9)

then plug these into the slope formula:

`m=(9-5)/(1-0)=(4)/(1)=4`

So, the slope of the line is 4.

The next piece of information we need is the y-intercept. Conveniently, we used a point on the y-axis to solve for slope, so we already know that the line crosses the y-axis at (0, 5) or when y = 5.

Using these two pieces of information, we can finally construct an equation in the form y = mx + b :

y = 4x + 5