Question

What is the equation parallel to y= -1/5x + 3 and goes through the point (7,4)? Please show steps.

Answer 1

If two lines are parallel, it means that they will have the same gradient:

And remember, the equation of a line is y = mx +c

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So we know that the equation of the parallel line is:

y = -
`(1)/(5)`x + c through point (7, 4)

All we need to do now is to work out what c is

Note: at point (7, 4) x = 7 , and y = 4.

So to work out c, we substitute in the values of x and y, and solve:

y = -
`(1)/(5)`x + c

4 = -
`(1)/(5)` * 7 + c

4 = -1.4 + c

5.4 = c

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Finally, we just put the value of c back into the original equation

y = -
`(1)/(5)`x + 5.4

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Answer:

The equation of the a line parallel to y = -
`(1)/(5)`x + 3 through point (7,4)

is: y = -
`(1)/(5)`x + 5.4

Answer 2

Explanation:

If it's parallel, that means it has the same slope: -1/5.

Use point-slope form to write the equation:

y - 4 = -1/5 (x - 7)

If you wish to write in point-intercept form:

y - 4 = -1/5 x + 7/5

y = -1/5 x + 27/5