Question

The line has a slope of 2/3 and passes through the point (0, -4). What is the point-slope form of the line? A) y+4= 2/3(x - 0) B) y+4=3/2(x - 0) C) y = 2/3x + 8 D) 4x+10y = 18​

Answer 1

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Required answer:
`\bf{y=(2)/(3)x-4}`

Detailed solution:

Let's take a look at our givens.

This line:

• Has a slope of 2/3
• Passes through (0,-4), where -4 is the y-intercept

We can substitute this info into slope-intercept:

`\bf{y=\displaystyle(2)/(3)x-4}`

∴ the equation of the line is
`\bf{y=(2)/(3)x-4}`

Have a wonderful day!

`\small\boxed{\boxed{\star}}}`

Answer 2

✦ Given that

• A line has a slope of 2/3; it passes through the point (5,1)

✦ We need to find

• The point-slope form of the line

`\hrulefill`

`\longleftrightarrow\rm{y-y_1=m(x-x_1)}`

`\longleftrightarrow\rm{y-(-4)=\cfrac{2}{3}(x-0)}`

`\longleftrightarrow\rm{y+4=\cfrac{2}{3}x}`

Therefore the point slope form for this line is y + 4 = 2/3x.