Answer:
B) x-intercept: (6, 0)
y-intercept: (0, 7)
Step-by-step explanation:
Given equation: [tex]7x + 6y = 42[/tex]
What are the x- and y-intercepts?
The x-intercept is the point where the line intersects the x-axis. In short, it is when y = 0 — [tex](x, y) \Rightarrow (x, 0)[/tex]. The y-intercept is where the line intersects the y-axis, which is when x = 0 — [tex](x, y) \Rightarrow (0, y)[/tex].
Find the x-intercept (by substituting 0 for y):
[tex]\\\implies 7x + 6y = 42\\\\\implies 7x + 6(0) = 42\\\\\implies 7x = 42\\\\\implies \dfrac{7x}{7}=\dfrac{42}{7}\\\\\implies \boxed{x=6}[/tex]
Coordinate: [tex](6, 0)[/tex]
Find the y-intercept (by substituting 0 for x):
[tex]\\\implies 7x + 6y = 42\\\\\implies 7(0) + 6y = 42\\\\\implies 6y = 42\\\\\implies \dfrac{6y}{6}=\dfrac{42}{6}\\\\\implies \boxed{y=7}[/tex]
Coordinate: [tex](0, 7)[/tex]
