How do you graph 2x+6y =4 and compute xand yintercept form

To graph the equation 2x + 6y = 4 and find the x and y-intercepts, we need to convert the given equation into slope-intercept form, which is in the form of y = mx + b.

Step 1: Solve for y in terms of x:
2x + 6y = 4
6y = -2x + 4
y = (-2/6)x + 4/6
Simplifying further:
y = (-1/3)x + 2/3

Step 2: Now that the equation is in slope-intercept form, we can easily identify the y-intercept and the slope.

The y-intercept is the value of y when x is equal to 0. From the equation y = (-1/3)x + 2/3, we can see that the y-intercept is 2/3.

The slope (m) is the coefficient of x in the equation. In this case, the slope is -1/3.

Step 3: Plot the y-intercept (0, 2/3) on the graph.

Step 4: To find the x-intercept, we set y equal to zero (y = 0) and solve for x:
0 = (-1/3)x + 2/3
(-1/3)x = -2/3
Multiply both sides by -3/1 to isolate x:
x = (-2/3) * (-3/1)
x = 2

The x-intercept is the value of x when y is equal to 0. Hence, the x-intercept is 2.

Step 5: Plot the x-intercept (2, 0) on the graph.

Step 6: Connect the two points on the graph with a straight line. This line represents all the points that satisfy the equation 2x + 6y = 4.

Congratulations! You have graphed the equation 2x + 6y = 4 and found the x and y-intercepts.