Find the slope and y-intercept of the line. 18x + 4y = 112

Solution:

First method:

Given equation is 18x + 4y = 112

Divide the equation by 112 throughout

x/(56/9) + (y/28) = 1

Compare with (x/a) + (y/b) = 1 where a is x intercept and b is y intercept

Hence x - intercept is = 56/9 and y - intercept = 28

Now the given equation can be compared to the general form Ax + By + C = 0

slope m = -A/B

thus the slope of the line is -18/4 = -9/2

Second method:

Given the equation is 18x + 4y = 112, now we know that x and y intercepts are the points on x and y axis respectively.

Thus to get the x - intercept put y = 0 in the given equation

∴ 18x + 4(0) = 112 ⇒ 18x = 112

⇒ x = 112/18 = 56/9

⇒ x intercept = 56/9

And to get the y intercept put x = 0 in the given equation,

∴ 18(0) + 4y = 112 ⇒ 4y = 112

⇒ y = 28

⇒ y intercept = 28

Now to find the slope, the line equation can be converted to slope intercept form that is y = mx + c

⇒ 4y = - 18x + 112

⇒ y = (-9/2)x + 28

∴ Slope m = -9/2

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Find the slope and y-intercept of the line. 18x + 4y = 112

Summary:

The x- and y-intercept of the line. 18x + 4y = 112 are 56/9 and 28 and slope is -9/2