Question

Find the equation of a line that passes through (1,11) and is parallel to the graph of y=2x+3 Write the equation in slope-intercept form, if possible.

Answer 1

y = -8x + 3

Explanation:

Firstly, plug in the point and slope into the slope-intercept equation format:

When lines are parallel to one another, their slopes are the same. But they have different y-intercepts. To explain further, slope is the angle of measure of a line from a horizontal standpoint and knowing that parallel angles must have the same angle, it can be concluded that parallel lines would have the same slope or in other words, an equal slope.

Now solving, use algebraic concepts:

11 = -8(-1) +b (Now solve for b)

11 = 8 + b (Subtract 8 from both sides) (Use the "Right" to "Left")

-8 -8

3 = b (Switch terms)

b = 3

Now let's write the equation with only slope and y-intercept.

Getting the result of:

y = -8x + 3

Answer 2

Notice that the given line is in slope-intercept form, therefore its slope is 2.

Now, we know that parallel lines have the same slope, using the slope-point formula for the equation of a line we get:

`y-11=2(x-1)\text{.}`

Taking the above to its slope-intercept form we get:

`\begin{gathered} y-11=2x-2, \\ y-11+11=2x-2+11, \\ y=2x+9. \end{gathered}`

Answer:

`y=2x+9.`