SOLUTION: Maria wrote the equation of a line that has a slope of Four-thirds and passes through point (3, 5). Which statement is true? The y-intercept is 4. The slope-intercept equation is

Algebra ->  Linear-equations -> SOLUTION: Maria wrote the equation of a line that has a slope of Four-thirds and passes through point (3, 5). Which statement is true? The y-intercept is 4. The slope-intercept equation is      Log On


   

Question 1158144: Maria wrote the equation of a line that has a slope of Four-thirds and passes through point (3, 5). Which statement is true?
The y-intercept is 4.
The slope-intercept equation is y = four-thirds x + 1.
The point-slope equation is y minus 3 = four-thirds (x minus 5).
The line also passes through the point (0, - 2).
Found 2 solutions by Edwin McCravy, josmiceli:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
We are given a point and the slope, so we use the point slope form
for an equation of a line:

matrix%281%2C3%2Cy-y%5B1%5D%2C%22%22=%22%22%2Cm%28x-x%5B1%5D%29%29

where we substitute the given slope for m and the given point for (x11).  
[We do not substitute for x and y, but leave them variable.]

matrix%281%2C3%2Cy-5%2C%22%22=%22%22%2Cexpr%284%2F3%29%28x-3%29%29

Distribute the 4/3:

matrix%281%2C3%2Cy-5%2C%22%22=%22%22%2Cexpr%284%2F3%29x-4%29

Add 5 to both sides

matrix%281%2C3%2Cy%2C%22%22=%22%22%2Cexpr%284%2F3%29x%2B1%29%29

Now it's in the slope-y-intercept form where the slope is 4/3 and the
y-intercept is 1

We'll check the choices:
The y-intercept is 4.
That's wrong because the y-intercept is 1, not 4.
The slope-intercept equation is y = four-thirds x + 1.
That's true because that's what we got.  So we have the answer. 
But let's see why the others are false anyway.
The point-slope equation is y minus 3 = four-thirds (x minus 5).
That's wrong because that has the x1 and y1 switched.
The line also passes through the point (0, - 2).
Let's substitute that and see why it's false:

matrix%281%2C3%2Cy%2C%22%22=%22%22%2Cexpr%284%2F3%29x%2B1%29%29
matrix%281%2C3%2C-2%2C%22%22=%22%22%2Cexpr%284%2F3%290%2B1%29%29
matrix%281%2C3%2C-2%2C%22%22=%22%22%2C0%2B1%29%29
matrix%281%2C3%2C-2%2C%22%22=%22%22%2C1%29%29

That's certainly false.

Edwin

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
( 3,5 )
+m+=+4%2F3+
-------------------
Use the general point-slope formula
+%28+y+-+5+%29+%2F+%28+x+-+3+%29+=+4%2F3+
Multiply both sides by +3%2A%28+x+-+3+%29+
+3%2A%28+y+-+5+%29+=+4%2A%28+x+-+3+%29+
+3y+-+15+=+4x+-+12+
+3y+=+4x+%2B+3+
+y+=+%28+4%2F3+%29%2Ax+%2B+1+
-------------------------------
(1) false, the y-intercept is 1
(2) true
(3) false
(4)
( 0, -2 )
+y+=+%28+4%2F3+%29%2Ax+%2B+1+
+-2+=+%28+4%2F3+%29%2A0+%2B+1+
+-2+=+1+ false
---------------------
Only (2) is true