Question

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Find the gradient of the linear relation

Answer 1

• 3y-5x=10

Isolate y

• 3y=5x+10
• y=5/3x+10/3

Compare to slope intercept form y=mx+b

Slope=m=5/3

Answer 2

Answer:

$\dfrac{5}{3}$

Step-by-step explanation:

To find the gradient (slope) of the given linear relation, use arithmetic operations to isolate y:

Given relation:

$3y-5x=10$

Add 5x to both sides:

$\implies 3y-5x+5x=10+5x$

$\implies 3y=5x+10$

Divide both sides by 3:

$\implies \dfrac{3y}{3}=\dfrac{5}{3}x+\dfrac{10}{3}$

$\implies y=\dfrac{5}{3}x+\dfrac{10}{3}$

Slope-intercept form of a linear equation

$y = mx+b$

where:

• m is the slope (gradient)
• b is the y-intercept

Comparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.

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