Question

4x - 3y = -24

Answer 1

The x-intercept of the line is -6

The y-intercept of the line is 8

The slope of the line is $\frac{4}{3}$

Step-by-step explanation:

You can find x-intercept by substitute y in the equation by zero

You can find y-intercept by substitute x in the equation by zero

If the equation of the line is ax + by = c, then

1. x-intercept ⇒ put y = 0

ax + b(0) = c

ax = c ⇒ divide both sides by a

x = $\frac{c}{a}$

x-intercept = $\frac{c}{a}$

2. y-intercept ⇒ put 0 = 0

a(0) + by = c

by = c ⇒ divide both sides by b

y = $\frac{c}{b}$

y-intercept = $\frac{c}{b}$

3. Slope ⇒ put the equation in the form y = m x + c, m is the slope

ax + by = c ⇒ subtract ax from both sides

by = c - ax ⇒ divide both sides by b

y = $\frac{c}{b}$ - $\frac{a}{b}$ x

m = $-\frac{a}{b}$

Slope = $-\frac{a}{b}$

∵ 4x - 3y = -24

∵ ax + by = c

∴ a = 4 , b = -3 and c = -24

∵ x-intercept = $\frac{c}{a}$

∴ x-intercept = $\frac{-24}{4}$

∴ x-intercept = -6

∵ y-intercept = $\frac{c}{b}$

∴ y-intercept = $\frac{-24}{-3}$

∴ y-intercept = 8

∵ m = $-\frac{a}{b}$

∴ m = $-\frac{4}{-3}$

∴ m = $\frac{4}{3}$

The x-intercept of the line is -6

The y-intercept of the line is 8

The slope of the line is $\frac{4}{3}$

Learn more:

You can learn more about slope in brainly.com/question/9801816

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