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 = $\frac{y2-y1}{x2-x1}$

• (x1,y1): (5,6)
• (x2,y2): (8,4)

    Slope = $\frac{4-6}{8-5} =-\frac{2}{3}$

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

   $y - 6 = -\frac{2}{3} (x-5)$

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

   $y = -\frac{2}{3}(x-5)+6 =-\frac{2}{3}x+\frac{10}{3} +6\\y = -\frac{2}{3} x+\frac{10}{3}+\frac{18}{3} \\y = -\frac{2}{3}x+\frac{28}{3}$<-- slope-intercept form

Hope that helps!