what is the equation in standard form of the line that passes through the point (6, -1) and is parallel to the line represented by 8x + 3y =15?

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joaobezerra joaobezerra · Answer 1 · 2022-04-22T11:20:15+02:00

The equation in standard form of the line is given by:

[tex]\frac{8}{3}x + y = 15[/tex]

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, the line is parallel to 8x + 3y =15, hence the slope is given by:

[tex]m = -\frac{8}{3}[/tex]

It passes through the point (6, -1), hence:

y = mx + b

[tex]-1 = -\frac{8}{3} \times 6 + b[/tex]

b = 15

Hence:

[tex]y = -\frac{8}{3}x + 15[/tex]

In standard form:

[tex]\frac{8}{3}x + y = 15[/tex]

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