5. Find the x and y intercepts of each linear equation. Be sure to write your answers as ordered pairs.
a.
To find the x-intercept of a linear equation, we set y equal to zero and solve for x. The x-intercept is the point where the line intersects the x-axis.
To find the y-intercept, we set x equal to zero and solve for y. The y-intercept is the point where the line intersects the y-axis.
Let's consider the equation a.
a. To find the x-intercept, we set y = 0.
Therefore, the equation becomes:
2x + 3(0) = 6
2x = 6
x = 6/2
x = 3
So, the x-intercept is (3, 0).
Next, to find the y-intercept, we set x = 0.
Therefore, the equation becomes:
2(0) + 3y = 6
3y = 6
y = 6/3
y = 2
So, the y-intercept is (0, 2).
Therefore, the ordered pairs for the x and y-intercepts of equation a are:
x-intercept: (3, 0)
y-intercept: (0, 2).