"if a is not equal to 0, find the intercepts of the graph of y=ax+b in terms of a and b?"
hello, zuko here
Well, if a is not equal to zero, then the graph of y = ax + b is a straight line. To find the x-intercept, you set y equal to zero and solve for x. So, if we set y = 0, we get 0 = ax + b. Now, since a is not equal to zero, we can isolate x by subtracting b from both sides of the equation. This gives us -b = ax. Finally, dividing both sides by a, we find that x = -b/a. Therefore, the x-intercept is -b/a.
To find the y-intercept, we set x equal to zero and solve for y. So, if we set x = 0, we get y = a(0) + b, which simplifies to y = b. Thus, the y-intercept is just b.
So, in terms of a and b, the x-intercept is -b/a, and the y-intercept is b. But remember, a and b cannot intercept with your feelings, because those should stay positive!
To find the intercepts of the graph of y = ax + b in terms of a and b when a is not equal to 0, we need to consider the x-intercept and y-intercept separately.
1. X-intercept:
To find the x-intercept, we need to set y equal to 0 and solve for x.
So, we have 0 = ax + b.
This equation represents the x-coordinate where the graph intersects the x-axis.
To solve for x, we can isolate it by subtracting b from both sides of the equation:
ax = -b.
Next, divide each side of the equation by a to isolate x:
x = -b/a.
Therefore, the x-intercept is (-b/a, 0).
2. Y-intercept:
To find the y-intercept, we need to set x equal to 0 and solve for y.
So, we have y = a(0) + b.
Simplifying, we get y = b.
Therefore, the y-intercept is (0, b).
In summary:
- The x-intercept is (-b/a, 0).
- The y-intercept is (0, b).
These intercepts give us two points on the graph of y = ax + b.
To find the intercepts of the graph of y = ax + b in terms of a and b, we need to determine the points where the line intersects the x-axis and y-axis.
1. X-Intercept:
The x-intercept is the point at which the line intersects the x-axis. To find the x-intercept, we set y = 0 and solve for x. So, we have:
0 = ax + b
To solve for x, we isolate it by subtracting b from both sides of the equation:
ax = -b
Divide both sides by a:
x = -b/a
Therefore, the x-intercept is (-b/a, 0).
2. Y-Intercept:
The y-intercept is the point at which the line intersects the y-axis. To find the y-intercept, we set x = 0 and solve for y.
y = a(0) + b
y = b
Therefore, the y-intercept is (0, b).
In summary, the intercepts of the graph of y = ax + b in terms of a and b are:
X-Intercept: (-b/a, 0)
Y-Intercept: (0, b)
The y intercept is where the line hits the y axis.
That is when x = 0
so
y = 0 x + b = b
The x intercept is where the line hits the x axis.
That is when y = 0
0 = a x + b
so
x = -b/a
(That is why a can not be equal to 0. If it were the x axis intercept would be undefined. This makes sense because if a = 0 then y = b, a constant which is a horizontal line.)