Question

Write the equation of the line, in standard form, that has an x-intercept of 2 and is parallel to 2x + y = -5. In

Answer 1

You're told that the x-intercept is 2. What is the coordinate at that point?
You're also given the equation of a line, \(2x + y = -5\). What is the slope of that line?

Answer 2

m=-2

Answer 3

Right! The coordinate of the x-intercept is?

Answer 4

I'm not sure

Answer 5

The x-intercept is where the line crosses the x axis. Likewise, the y-intercept is where the line crosses the y-axis.
What is the y-value at any point along the x-axis? (Remember that the x-axis is the horizontal axis)

Answer 6

Using the given equation y=0

Answer 7

Right! But that's true regardless of what equation you're using. Remember that the point where the x-axis and y-axis intersect/cross is \((0,0)\).
Starting from that point \((0,0)\), if we go or down along the y-axis, we'll have points given by \((0,y)\); if we go left or right along the x-axis, we'll have points given by \((x,0)\).

Back to the question:
If we're told that the x-intercept is 2, what is the coordinate/point that represents that?

Answer 8

2,0

Answer 9

Great! Now what is the relationship between the slope of two parallel lines (which is the case for this problem)?

Answer 10

What do you mean by that?

Answer 11

Remember that for two lines that are perpendicular, their slopes are negative reciprocals of each other (for example, \(m=-2\) and \(m=\dfrac{1}{2}\) and thus, multiply together to equal -1.

What is the relationship between the slopes of two parallel lines?

Answer 12

Same

Answer 13

As in parallel have same slope

Answer 14

Yep! Parallel lines have the same slope; perpendicular lines have slopes that are negative reciprocals of one another.

Now you have all of the information that you need--a point \((2,0)\) and a slope \(m=-2\) (which we know because we have the slope of the equation that's given to you),. Now you can plug this information into the equation of a line to get your equation, then convert it into standard form \(Ax+By=C\)

Answer 15

This is where I trip up

Answer 16

There are several forms of the equation of a line:

Slope-intercept form: \(y=mx+b\)
>>>Use this when you have a slope and y-intercept available


Point-slope form: \(y-y_1=m(x-x_1)\)
>>>>Use this when you have a point \((x,y)\) and a slope


Standard form: \(Ax+By=C\)
>>>Usually you'll use one of the two forms above to get to the standard form.

In this problem, the only information that we have is a point \((2,0)\) and a slope \(m=-2\). Which form of the equation for a line should we use?