Answer: The correct answer would be C. y= 4/5x+1
Step-by-step explanation:
[tex]y-intercept=\frac{47}{5}[/tex]
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-7-(4/5*(x+3))=0
STEP
1
:
4
Simplify —
5
Equation at the end of step
1
:
4
(y - 7) - (— • (x + 3)) = 0
5
STEP
2
:
Equation at the end of step 2
4 • (x + 3)
(y - 7) - ——————————— = 0
5
STEP
3
:
Rewriting the whole as an Equivalent Fraction
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 5 as the denominator :
y - 7 (y - 7) • 5
y - 7 = ————— = ———————————
1 5
Equivalent fraction: The fraction thus generated looks different but has the same value as the whole
Common denominator: The equivalent fraction and the other fraction involved in the calculation share the same denominator
3.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
(y-7) • 5 - (4 • (x+3)) 5y - 4x - 47
——————————————————————— = ————————————
5 5
Equation at the end of step
3
:
5y - 4x - 47
———————————— = 0
5
STEP
4
:
When a fraction equals zero :
4.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now, to get rid of the denominator, I multiply both sides of the equation by the denominator.
Here's how:
5y-4x-47
———————— • 5 = 0 • 5
5
Now, on the left hand side, the 5 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
5y-4x-47 = 0
Equation of a Straight Line
4.2 Solve 5y-4x-47 = 0
CalderonJ recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx + b" is the formula of a straight line drawn on a Cartesian coordinate system in which "y" is the vertical axis and "x" is the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 5y-4x-47 = 0 and calculate its properties
Notice that when x = 0 the value of y is 47/5 so this line "cuts" the y axis at y= 9.40000
y-intercept = 47/5 = 9.40000
Calculate the X-Intercept :
When y = 0 the value of x is 47/-4 Our line therefore "cuts" the x axis at x=-11.75000
x-intercept = 47/-4 = -11.75000
Calculate the Slope :
The slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 9.400 and for x=2.000, the value of y is 11.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 11.000 - 9.400 = 1.600 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 1.600/2.000 = 0.800
