Question

Write the equation of the line in fully
simplified slope-intercept form.

Answer 1

y = 2/3x - 6

Explanation:

Knowledge Needed

Slope-Intercept form: y = mx + b

Leave y and x as variables as it is easier for graphing.

m is the slope, or how much the y-value changes every timer the x-value increases by 1.

b is the y-intercept, or the x-value of the line when it has a x-value of 0 (when it hits the y-axis.)

Question

Using this information, lets first find the slope.

To find the slope, we can use the slope formula. Use any two sets of points to plug into the formula.

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

I'll use the points:

(3, -4)

and

(6, -2)

Because they are marked.

Plug in your two y-values into the numerator and two x-values into the denominator.

`(-2 - - 4)/(6 - 3)`

2/3

So, we have 2/3 as a slope. We can start writing the equation in slope-intercept form.

y = 2/3x + b

To solve for b, we can either examine the graph or solve it algebraically. However, if the graph is more complex we can't just look at it.

What is the x-value of the line when it touches the y-axis, or the bold vertical line?

-6

We know the y-intercept is -6.

y = 2/3x - 6