The x-intercept of the line is -6
The y-intercept of the line is 8
The slope of the line is [tex]\frac{4}{3}[/tex]
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 = [tex]\frac{c}{a}[/tex]
x-intercept = [tex]\frac{c}{a}[/tex]
2. y-intercept ⇒ put 0 = 0
a(0) + by = c
by = c ⇒ divide both sides by b
y = [tex]\frac{c}{b}[/tex]
y-intercept = [tex]\frac{c}{b}[/tex]
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 = [tex]\frac{c}{b}[/tex] - [tex]\frac{a}{b}[/tex] x
m = [tex]-\frac{a}{b}[/tex]
Slope = [tex]-\frac{a}{b}[/tex]
∵ 4x - 3y = -24
∵ ax + by = c
∴ a = 4 , b = -3 and c = -24
∵ x-intercept = [tex]\frac{c}{a}[/tex]
∴ x-intercept = [tex]\frac{-24}{4}[/tex]
∴ x-intercept = -6
∵ y-intercept = [tex]\frac{c}{b}[/tex]
∴ y-intercept = [tex]\frac{-24}{-3}[/tex]
∴ y-intercept = 8
∵ m = [tex]-\frac{a}{b}[/tex]
∴ m = [tex]-\frac{4}{-3}[/tex]
∴ m = [tex]\frac{4}{3}[/tex]
The x-intercept of the line is -6
The y-intercept of the line is 8
The slope of the line is [tex]\frac{4}{3}[/tex]
Learn more:
You can learn more about slope in brainly.com/question/9801816
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