Question

Write an equation of the line in slope-intercept form. JY 1 (3, 3) (0, 2) 2 4
y=​

Answer 1

Correct answer: y =
`(1)/(3)`x + 2

To find out the slope, you would need to remember this slope formula:
`(y_(2)-y_(1))/(x_(2)-x_(1))`. We can use the two points provided on the graph to figure out the slope. We can label (3, 3) as
`x_(1)` and
`y_(1)`, and (0, 2) as
`x_(2)` and
`y_(2)`. Now we can plug these numbers into the slope formula to find out the slope:

m =
`(y_(2)-y_(1))/(x_(2)-x_(1))` →
`(2-3)/(0-3)` →
`(-1)/(-3)` →
`(1)/(3)`

To find out the y-intercept, just substitute (3, 3) into the slope-intercept formula ( y = mx + b ) with the slope that is substituted for 'm' that we already solved earlier.

y = mx + b

(3) =
`(1)/(3)`(3) + b

3 = 1 + b

2 = b

You can also prove this true by looking at the graph provided. The line intersects at the y-axis at 2.

Now we know that m =
`(1)/(3)` and b = 2, we can substitute it into the slope-intercept formula. Thus, the answer is y =
`(1)/(3)`x + 2.

Hope this helps you! Let me know if you have any more questions related to this problem.