Question

Can you break down how to solve the problem ?

Answer 1

A. y =
`(-5x)/(2)` - 1

Explanation:

Given parameters:

Equation of the line:

5x + 2y = 12

Coordinates = -2, 4

Unknown:

The equation of the line parallel to this line = ?

• To solve this problem, first, we need to find the slope of the given line.

Every linear equation have the formula: y = mx + c

m is the slope of the line, c is the y- intercept

5x + 2y = 12

Express this equation as y = mx + c

2y = -5x + 12

y =
`(-5)/(2)x` + 6

The slope of this line is
`(-5)/(2)`

• Now, any line that is parallel to another will not cut or cross it at any point. This simply implies they have the same slope.

Slope of the line parallel is
`(-5)/(2)`

• Our new line will also take the form y=mx + c,

Coordinates = -2, 4, x = -2 and y = 4

m is
`(-5)/(2)`

Now let us solve for C, the y-intercept;

4 = - 2 x
`(-5)/(2)` + C

4 = 5 + C

C = -1

The equation of the line is therefore;

y =
`(-5x)/(2)` - 1