Question

Write the equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3

Answer 1

The equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3 is:

`\mathbf{y=-(2)/(3)x+1}`

Explanation:

We need to write equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3.

The equation for slope-intercept form is:
`y=mx+b`

where m is slope and b is y-intercept.

We are given slope m = -2/3 and we need to find y-intercept i.e b to write equation of line.

Using point (3,-1) and slope m=-2/3 we can find y-intercept i.e b

`y=mx+b\\-1=-(2)/(3)(3)+b\\-1=-2+b\\b=-1+2\\b=1`

So, y-intercept b = 1

The equation of the line, in slope-intercept form, that passes through (3,-1) and has a slope = -2/3 is:

`y=mx+b\\\mathbf{y=-(2)/(3)x+1}`