Answer:
[tex]\bf\mathsf{X-intercept=(\frac{25}{3},\:0)}[/tex]
Y-intercept = (0, -5)
Step-by-step explanation:
Given the linear equation in standard form, 3x - 5y = 25, for which we must determine its x- and y-intercepts.
It is essential to understand what the intercepts mean relative to the given equation and its location on the graph.
The x-intercept is the point where the graph crosses the x-axis. Hence, its coordinates are often represented by (a, 0). Thus, the x-intercept provide the value of x when the value of the y-coordinate is 0.
Now, we can solve the x-intercept by setting y = 0:
3x - 5y = 25
3x - 5(0) = 25
3x - 0 = 25
3x = 25
Divide both sides by 3 to solve for x:
[tex]\large\mathsf{\frac{3x}{3}\:=\:\frac{25}{3}}[/tex]
[tex]\bf\mathsf{x=\:\frac{25}{3}}[/tex]
Therefore, [tex]\bf\mathsf{X-intercept=(\frac{25}{3},\:0)}[/tex] .
The y-intercept is the point where the graph crosses the y-axis. Hence, its coordinates are often represented by (0, b ). Thus, the y-intercept provide the value of y when the value of the x-coordinate is 0.
Now, we can solve the y-intercept by setting x = 0:
3x - 5y = 25
3(0) - 5y = 25
0 - 5y = 25
-5y = 25
Divide both sides by -5 to solve for y:
[tex]\large\mathsf{\frac{-5y}{-5}\:=\:\frac{25}{-5}}[/tex]
y = -5
Therefore, the y-intercept is (0, -5).
