Question

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Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.

Answer 1

I hope this helps, you can ask any questions for clarification

Answer 2

To write something in slope-intercept form

⇒ need to know what slope-intercept looks like:
`y = mx +b`

• m: the value of the slope
• b: y-intercept

Let us first find the slope:

Formula of slope =
`(y2-y1)/(x2-x1)`

• (x1,y1): (5,6)
• (x2,y2): (8,4)

Slope =
`(4-6)/(8-5) =-(2)/(3)`

Lets now write in point-slope form:

⇒
`(y-y0)=m(x-x0)`

• (x0,y0): any point on the line --> (5,6)
• m: value of slope

`y - 6 = -(2)/(3) (x-5)`

To write it into slope-intercept form, we must solve for y

`y = -(2)/(3)(x-5)+6 =-(2)/(3)x+(10)/(3) +6\\y = -(2)/(3) x+(10)/(3)+(18)/(3) \\y = -(2)/(3)x+(28)/(3)`<-- slope-intercept form

Hope that helps!