Question

A line passes through the point (2, 8) and has a slope of 3.

a. What is the y-intercept of the line?
b. What is the x-intercept of the line?
c. Write an equation for the line in slope-intercept form.

Answer 1

a. 2

b.
`(-2)/(3)`

c. y=3x+2

Explanation:

a. The y-intercept of the line can be found by using slope intercept form, the given slope, and the given point.

Slope intercept form: y=mx+b

Rearranging for b:

b=y-mx

b=8-3*2=8-6=2

So the y-intercept is 2.

b. The x intercept is found where the function crosses the x-axis. At this point, the y-coordinate will be zero. To find this value, rearrange slope intercept form to solve for x and use y=0 for y in the equation along with the given slope and calculated y-intercept.

Rearranged slope intercept form:

y=mx+b

y-b=mx

`x=(y-b)/(m)=(0-2)/(3)=(-2)/(3)`

c. The equation for the line in slope intercept form will use the given slope, and the calculated y-intercept.

y=mx+b

y=3x+2

Answer 2

A). (0,2) or b=2

To find the y intercept it is easiest to put the point into point slope form, y-y1=m(x-x1) and converting it to slope intercept form

y-8 = 3(x-2)
y-8 = 3x-6
y=3x+2

Slope intercept form is y=mx+b and b is the y intercept this means that there is a y intercept of 2

b). -2/3 or (-2/3,0)

We can use our slope intercept form from part a to find the x intercept

Since the x intercept is the point where y equals 0 we can input y as 0 and solve

Y=3x+2
0=3x+2
-2=3x
-2/3=x

This means that there is an x intercept of -2/3

c). y=3x+2

We had originally solved this in part a