How do you graph 3x plus 4y equals 5?

Answer 1

3x + 4y = 5

To find the x-intercept, let x = 0

3(0) + 4y = 5

4y = 5

y = 5/4

The line passes through (0, 5/4), so y-intercept is 5/4.

To find x-intercept, let y = 0

3x + 4(0) = 5

3x = 5

x = 5/3

The line passes through (5/3, 0), so x-intercept is 5/3.

Plot (0, 5/4) and (5/3, 0). Draw a straight line through them.

Or,

3x + 4y = 5

3x - 3x + 4y = 5 - 3x

4y = -3x + 5

4y/4 = (-3x + 5)/4

y = (-3/4)x + 5/4

So the slope will be -3/4 and the y-intercept is 5/4; (0, 5/4)

We find the x-intercept when y = 0, so

0 = (-3/4)x + 5/4

0 - 5/4 = (-3/4)x + 5/4 - 5/4

-5/4 = (-3/4)x

(-5/4)/(-3/4) = [(-3/4)x]/(-3/4)

5/3 = x ; (5/3, 0)

Thus, the line passes through the points (0, 5/4) and (5/3, 0).