SOLUTION: #1 Write the equation of a line in y= form, through the point (-2,5) and (3,4). I have found the first part of the problem by doing y2-y1 over x2-x1 and that gave me -1/5. B

Algebra ->  Linear-equations -> SOLUTION: #1 Write the equation of a line in y= form, through the point (-2,5) and (3,4). I have found the first part of the problem by doing y2-y1 over x2-x1 and that gave me -1/5. B      Log On


   

Question 116228: #1
Write the equation of a line in y= form, through the point (-2,5) and (3,4).
I have found the first part of the problem by doing y2-y1 over x2-x1 and that gave me -1/5. But I do not understand how to do the rest of the problem and write out the answer.
#2
Find the slope and y-intercepts of the given line: 4x-5y=16.
What steps do I take to solve this problem?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
One equation you can take advantage of is the form:
.
y+=+mx+%2B+b
.
This is called the slope-intercept form and it is the equation of a line in which m, the multiplier
of the x term, is the slope of the line and b is the value on the y-axis where the line crosses the y-axis.
.
In the first problem you correctly found that the slope was -1/5. You can substitute this
value into the slope-intercept form and you get that the equation for the line then becomes:
.
y+=+-%281%2F5%29x+%2B+b
.
At this point you just need to find b to complete the equation. To do this you can use
either of the two points that you were given. Let's use the point (3, 4). This tells you
that when x = 3 and y = 4 the equation must balance. So substitute 3 for x and 4 for y and
the equation becomes:
.
4+=+-%281%2F5%29%2A3+%2B+b
.
Multiply out the first time on the right side to get:
.
4+=+-3%2F5+%2B+b
.
Solve for b by adding +3/5 to both sides. [This gets rid of the -3%2F5 on the right
side.] On the left side when you add 4+%2B+3%2F5 you get 23%2F5. This results in
b = 23%2F5. So we can substitute this value for b into the slope-intercept form to get:
.
y+=+-%281%2F5%29x+%2B+23%2F5
.
Let's check it out by finding if (-2,5) is a point on the line. Substitute into the slope-intercept
form -2 for x and 5 for y and see if the equation balances.
.
5+=+-%281%2F5%29%28-2%29+%2B+23%2F5
.
Replace 5 by its equivalent 25%2F5 and this becomes:
.
25%2F5+=+-%281%2F5%29%28-2%29+%2B+23%2F5
.
Multiply out the first term on the right side:
.
25%2F5+=+2%2F5+%2B+23%2F5
.
The two terms on the right side add to 25%2F5 and so the equation is true. This checks
the equation y+=+-%281%2F5%29x+%2B+23%2F5
.
The second problem asks you to find the slope and y-intercept of the equation:
.
4x-5y=16
.
Let's work this into the form y+=+mx+%2B+b
.
Begin by subtracting 4x from both sides to get rid of the 4x on the left side. This changes
the equation to:
.
-5y+=+-4x+%2B+16
.
Make the term on the left side positive by multiplying both sides (all terms) by -1 to get:
.
5y+=+4x+-+16
.
Solve for y by dividing both sides (all terms) by 5 to get:
.
y+=+%284%2F5%29x+-16%2F5
.
Note that this is in the slope-intercept form. So just by looking at it you can tell that
the slope is 4%2F5 [you can tell that because it is the multiplier of x which is the slope.]
.
And you can tell that the y-intercept is -16%2F5 because that is the constant term
in this slope-intercept equation.
.
Hope this helps you to understand these problems. Since it's late, please check my math to
make sure I didn't make a dumb error in the numbers. The basic process of using the slope-
intercept form is correct.
.