Question

select the equation of a straight line that is parallel to 4y=3x+5

Answer 1

Answer:

4y+5=3x, 4 y + 5 = 3 x .

Answer 2

Given,

Equation of a line:

4y = 3x + 5.

To find,

Equation of a straight line that is parallel to the given line.

Solution,

Here, the given line is,

4y = 3x + 5     ...(1)

The slope-intercept form of a line is given as,

y = mx + c     ...(2)

The given equation of the line (1) can be converted to the slope-intercept form of a line as follows.

$y=\frac{3}{4} x+\frac{5}{4}$

Comparing it with the equation in (2), the slope of the given line is,

$m=\frac{3}{4}$

Now, the slope of a line is its inclination or the steepness in the coordinate plane.

So, all the lines with the same slope as that of the given line will be parallel to it.

If we substitute $m=\frac{3}{4}$ in (2), we get,

$y =\frac{3}{4} x+c$

So, all the lines of this form will be parallel to the given line.

Therefore, all the lines of the form $y =\frac{3}{4} x+c$ will be parallel to 4y = 3x + 5.