Find an equation of the line passing through the pair of points. Write the equation in the form Ax+By=c?

Let the general equation of a straight line be: y = mx + c ......... (this is the slope-intercept form)

Since (4, 9) is on the line:

9 = 4m + c ............................(1)

And since (3, 5) is also on the line:

5 = 3m + c ...........................(2)

Subtracting eqn. (2) from (1), we have:

9 = 4m + c

5 = 3m + c

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4 = m

Substituting the value of m in eqn. (1) and solving for c:

9 = 4*4 + c

c = 9 - 16 = -7

Substituting the values of m and c in the original equation, we get:

y = 4x - 7

y - 4x = -7

4x - y = 7

Solution: The equation of the line is 4x - y = 7

which is in the form: Ax + By = C, where A = 4, B = -1 and C = 7

The line through (x₁,y₁) and (x₂,y₂) is given by (x₁-x₂)(y-y₂) = (y₁-y₂)(x-x₂) which can be manipulated to the standard form (y₁-y₂)x - (x₁-x₂)y = y₁x₂ - x₁y₂.

Here we have (9-5)x - (4-3)y = 9×3 - 4×5, which simplifies to 4x - y = 7

Graph: https://www.desmos.com/calculator/6vgf0e3ua0

m = (9 - 5) / (4 - 3)

m = 4

y = mx + b

9 = 4 * 4 + b

9 = 16 + b

-7 = b

y = 4x - 7

-4x + y = -7

4x - y = 7