Answer:
X-intercept: [tex](\frac{14}{3}, 0)[/tex].
Y-intercept: (0, 7) ⇒ Option B.
Step-by-step explanation:
I'm not certain whether the question asks for either the x-intercept or the y-intercept, but I will provide the answers for both since none of the given options matches the coordinates of the x-intercept.
The x-intercept is the point on the graph where it crosses the x-axis, with coordinates of (a, 0). The x-intercept is the value of x when y = 0.
Given the linear equation in standard form, 3x + 2y = 14, set y = 0 to solve for the x-intercept:
3x + 2y = 14
3x + 2(0) = 14
3x + 0 = 14
3x = 14
Divide both sides by 3 to solve for x:
[tex]\frac{3x}{3} = \frac{14}{3}[/tex]
[tex]x = \frac{14}{3}[/tex]
Therefore, the x-intercept is [tex](\frac{14}{3}, 0)[/tex]. None of the given option matches the value of the x-intercept.
The y-intercept is the point on the graph where it crosses the y-axis, and has coordinates of (0, b). It is the value of y when x = 0.
Set x = 0, and substitute into the given equation.
3x + 2y = 14
3(0) + 2y = 14
0 + 2y = 14
2y = 14
Divide both sides by 2 to solve for y:
[tex]\frac{2y}{2} = \frac{14}{2}[/tex]
y = 7
Therefore, the y-intercept is (0, 7), which matches Option B.
