Write the equation in standard form of the line that passes through P (5, - 7) and has slope of -1/5?

Answer 1

There're two ways of going about solving this question, which are... essentially the same, just using variations of the same formula.

1. Firstly, let's do a review of the first equation, the basic equation in a straight line formula.

y = mx + c

y: value of the y coordinate at a point
m: value of the gradient/slope
x: value of the x coordinate at a point
c: y-intercept, i.e. the point where the line cuts through the y-axis.

From here, using your given coordinate (5, -7) and your slope value, -1/5:

-7 = (-1/5)*5 + c
-7 = -1 + c
-7 + 1 = c
c, y-intercept = -6

Substituting the value of c = -6 in y = mx + c, you get

y = (-1/5)x -6

2. You can derive this second formula from the equation of straight line formula:

y-y1 = m(x-x1)

y1 and x1 are values of your given coordinate should you choose to use them in the equation, i.e. (x1, y1). Yep? Okay. So, using your coordinate P (5, -7), this means that your x1 = 5 and your y1 = -7. Substitute the values into your equation:

x1, value of x-coordinate = 5
y1, value of y-coordinate = -7
m, slope/gradient = -1/5

y - (-7) = (-1/5)(x - 5)
y + 7 = (-1/5)x + 1
y = (-1/5)x -6

With reference to the first formula,
y = mx + c

m, slope/gradient = -1/5
c, y-intercept = -6

With this formula, you don't have to worry about the added unknown (be it c or b or z, really) that serves as the symbol for the y-intercept. It's much less confusing. In the end, you get the same answer, so, really, it's entirely up to you.

Answer 2

There are two formulae you need to know to describe lines.

y = mx + b, where m is the slope and b is the y intercept. This is the standard form.

m = (y2-y1)/(x2 - x1)

You have the slope and two-and-a-half points. Every line has a point (0,b), which is your half point.

-1/5 = (b - -7)/(0 - 5)

-1/5 = (b + 7)/(-5)

-1/5 * -5 = b + 7

1 = b + 7

b = -6

Plugging that into the standard equation, you get:

y = -1/5x - 6

Test that on your known point.

y = -1/5(5) - 6

y = -1 - 6 = -7

Answer 3

given: slope[y]=-1/5
the line passes theough [5,-7]so for that point y=-7 and x=5

we know that
y=mx+c for a straight line
by putting the given values we get
-7=-1/5X5+c
from this equation c=-7+1
c=-6
so y=-1/5x-6
or, 5y+-x-30
so 5y+x+30=0..ans

Answer 4

Y + 7 = - (1/5) (x-5)
5y + 35 = -x +5
5y = -x -30
y = -(1/5)x - 6

Answer 5

yup, u use component slope form that is- y-y1=m(x-x1) so u plug the component into the equation and m as perfect so u get- y-3=7(x-4) so then u get y-3=7x-4 then y=7x-a million so y=7x-a million is youre answer. the (4,3) is (x1, y1) so u basically plug it into the component slope equation, want this enables!

Answer 6

y=-1/5x-6(slope-intercept)

5y=-x-30

5y+x=-30