Question

Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.

Answer 1

Answer: y = 3x+2

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Step-by-step explanation:

The equation y = 3x-1 is in slope-intercept form y = mx+b

• m = 3 = slope
• b = -1 = y intercept

Parallel lines have equal slopes, but different y intercepts.

The answer will also have a slope of m = 3.

Plug that slope value, and the coordinates of the given point
`(x_1,y_1) = (1,5)` , into the point-slope formula below.

Solve for y.

`y - y_1 = m(x - x_1)\\\\y - 5 = 3(x - 1)\\\\y - 5 = 3x - 3\\\\y = 3x - 3+5\\\\y = 3x + 2\\\\`

That's how we arrive at the answer of y = 3x+2

As a check, plugging x = 1 into that answer should get us y = 5.

It confirms that the point (1,5) is on this line.