Question

Find the x​ - and y​ -intercepts of the graph of the linear equation 2 x plus 3 y is equal to 2x+3y=12

Answer 1

x-intercept is 6 [(6, 0) is the point]

y-intercept is 4 [(0, 4) is the point]

Explanation:

To find the x-intercept, we can set y equal to 0 and solve for x. This works because the x-intercept is the point of the graph where the line crosses the x-axis (meaning y is equal to 0 at this point. So, if we set y=0 and solve, we get this:

`2x+3(0)=12\\2x=12\\x=6`

So, the x-intercept is 6; if it is written as a point, it is (6, 0) since y is 0

To find the y-intercept, we can set x equal to 0 and solve for y. This works the same way - x is equal to 0 at the point where the line crosses the y-axis. If we set x=0 and solve, we get this:

`2(0)+3y=12\\3y=12\\y=4`

So, the y-intercept is 4; if it is written as a point, it is (0, 4) since x is 0