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Answer: y=2x-1

We know that the equation of a line is y = mx + b, where m is the gradient and b is the y-intercept.

First to find the gradient, we use the formula y2-y1/x2-x1.

x1 and y1 being the first set of coordinates (2,3) and x2 and y2 being the second set (4,7)

Now we sub in:
m=7-3/4-2
m=4/2
m=2

This is our gradient and we can put it into the equation: y=2x+b

Now we find the y-intercept (b). Since the y-intercept isn’t shown, we can sub in the coordinates to find it.

y=2x+b
Sub (2,3)
3=2(2)+b
3=4+b
-1=b

Sub (4,7)
7=2(4)+b
7=8+b
-1=b

Subbing in both coordinates gives us -1 as the y-intercept, so the finished equation is: y=2x-1

Answer:

y = 2x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = B(2,3) and (x₂, y₂ ) = A(4, 7)

m = [tex]\frac{7-3}{4-2}[/tex] = [tex]\frac{4}{2}[/tex] = 2, thus

y = 2x + c ← is the partial equation of the line

To find c substitute either of the 2 points into the partial equation

Using (2, 3), then

3 = 4 + c ⇒ c = 3 - 4 = - 1

y = 2x - 1 ← equation of line

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