Question

The x and y intercepts of the line 4x + 7y = 28 are

Ops

A)7 units and 4 units
B)0 units and 3 units
c)3 units and 0 units
D)4 units and 7 units​

Answer 1

The x and y intercepts of the line 4x + 7y = 28 are (7 - 7/4y) and (4 - 4/7x) respectively.

Given : 4x + 7y = 28

To Find : Value of x and y

Solution :

Solving for x,

4x + 7y = 28

4x = 28 - 7y

x = (28 - 7y) / 4

x = 7 - 7/4y

Solving for y,

4x + 7y = 28

7y = 28 - 4x

y = (28 - 4x) / 7

y = 4 - 4/7x

Therefore, the values of the x and y intercepts of the line 4x + 7y = 28 are (7 - 7/4y) and (4 - 4/7x) respectively.

Answer 2

The given line has x-intercept = 7 units and y-intercept = 4 units. (option A)

Given,

Line:

4x + 7y = 28.

To find,

The x- and y-intercepts of the given line.

Solution,

Here, we can see that the equation of a line is given, which is

$4x+7y=28 \hfill ...(1)$

To find the intercepts on x- and y-intercepts, we first need to convert the given equation into the intercept form.

Now, the intercept form of the equation of any line is given as

$\frac{x}{a} +\frac{y}{b} =1 \hfill ...(2)$

where,

a = x-intercept, and

b = y-intercept.

So, to convert (1) into the intercept form, we need to divide it by 28, on both sides. Thus, (1) can be written as

$\frac{4x}{28} +\frac{7y}{28} =\frac{28}{28}$

Simplifying,

$\frac{x}{7} +\frac{y}{4} =1$

Comparing the above equation with (2), we see that,

a = 7, and

b = 4.

So,

x-intercept = 7 units,

y-intercept = 4 units.

Therefore, the given line has x-intercept = 7 units and y-intercept = 4 units. (option A)

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