Equation of a line question?

Question

Can someone please help me with this question that I am having trouble figuring out, it is dealing with trying to determine the equation of a line with this given information, I have to put the final answer in standard form;

(1,7), and a slope of 4/5.
The fraction for a slope is what confuses me as how to solve this question, thanks.

Answer 1

Use the point-slope form:

y - 7 = 4/5(x -1) <------- point-slope form

Then, if you want to put this in slope-intercept form, solve for y:

y - 7 = (4/5)x - 4/5

y = (4/5)x - 4/5 + 7

y = (4/5)x - 4/5 + 35/5

y = (4/5)x + 31/5 <------ slope-intercept form

And of course, you can always write it in standard form. Start by multiplying through by 5:

5y = 4x + 31

-4x + 5y = 31 <-------standard form

Answer 2

When the equation is in standard form, ax + by = c, the slope is -a/b. Since the slope you need is 4/5, your equation should start 4x - 5y = c. To find c, plug in the point:

4(1) - 5(7) = c
4 - 35 = c
-31 = c

so 4x - 5y = -31

Answer 3

Start with slope intercept...

y = (4/5)x + ?

Which value would yield (1, 7)?

y = (4/5)x + 31/5

Now, convert to standard form.

5y - 4x = 31

Answer 4

y - b = m.(x - a)
y - 7 = (4/5).(x - 1)
y = (4/5).x - 4/5 + 35/5
y = (4/5).x + 31/5
This, if desired, may be written as:-
5y = 4x + 31
4x - 5y + 31 = 0

Answer 5

Slope intercept for is: y = mx + b in view which you have each and all of the values different than b you may fill in and remedy for b. y = mx + b -5 = (4/5)(0) + b -5 = 0 + b b = -5 So, y = (4/5)x - 5

Answer 6

y-y1=m(x-x1)

y-7=4/5(x-1), mult. by five we get:

5y-35=4x-4
4x-5y+31=0.....your sol.