Question

Find the y-intercept and slope of the line below. Then write the equation is slope intercept form (y=mx+b).

Answer 1

`y\text{ = }(-3)/(2)x\text{ + 6}`

Step-by-step explanation:

The y-intercept is the value of y when x = 0

To identify y-intercept on a graph, we will check for the the value of y when the line crosses the y axis

From the graph, the line crosses the y axis at y = 6

Hence, the y-intercept is 6

To get the slope, we will pick any two points on the line.

Using points (0, 6) and (4, 0)

Applying the slope formula:

`m\text{ = }(y_2-y_1)/(x_2-x_1)`
`\begin{gathered} x_1=0,y_1=6,x_2=4,y_2\text{ = }0 \\ m\text{ = }\frac{0\text{ - 6}}{4\text{ - 0}} \\ m\text{ = }(-6)/(4) \\ m\text{ = slope = -3/2} \end{gathered}`

NOTE: the slope is negative because it is going from up to down (moving downwards)

The equation of slope in intercept form: y = mx + b

m = slope = -3/2

b = y-intercept = 6

The equation in y-intercept becomes:

`y\text{ = }(-3)/(2)x\text{ + 6}`