**Q:** What is the equation of a line?

**A:** The equation of a line is **y=mx+b**, where

**m = slope**

**b = y-intercept**

**Q:** What is slope?

**A:** The slope of a line is a measure of how steep the line is. A larger slope means that the line is steeper, while a smaller slope corresponds to a flatter line.

The equation for slope is:

So essentially, slope is just **the change in y divided by the change in x**.

Let’s look at a graph with three different lines. Note that the green line has the largest slope, while the blue line has the smallest slope.

**Q:** What is the y-intercept?

**A:** In the equation of a line, **y=mx+b**, the y-intercept is ** b**. It is the y-value where the line crosses the y-axis.

Using the same three lines, let’s find their y-intercepts.

Lastly, let’s look at the same three lines with their equations in **y=mx+b** form.

Any line is defined by just **two **pieces of information: the slope, **m**, and the y-intercept, **b**.

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**Q:** The equation of a line is y=2x -7. What is the y-intercept?

**A:** It is easy enough to simply compare the equation to the standard form, **y=mx+b**, and see that b = -7.

However, the general way **to find the y-intercept is to set x=0, and solve for y**.

y = 2(0) – 7

y = 0 – 7

y = -7

Either way you do it, the y-intercept is -7. This is the location where the line crosses the y-axis.

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**Q:** Can you show me how to find the slope of a line with the equation (y+3)=5(x-2)?

**A:** First, turn the equation into slope-intercept form, **y=mx+b**. Do this by isolating for **y **in the equation.

y + 3 = 5x – 10

y = 5x – 10 – 3

y = 5x – 13

Compare this to the general equation for a line: **y=mx+b**.

You should see that **m = 5** and b = -13. This means that the slope is 5.

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**Q:** Can you show me the steps on how to work this out? What is the y-intercept of a line with the equation (y-3)=5(x+2)? Thanks.

**A:** Again, turn the equation into slope-intercept form, y=mx+b, by isolating for y:

y – 3 = 5x + 10

y = 5x + 10 + 3

y = 5x + 13

Compare this to the general equation for a line: **y=mx+b**.

You should see that **b = 13**. The y-intercept is 13. This means the line crosses the y-axis at y=13.

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**Q:** What is the slope of a line that contains the two points (0,3) and (4,5) ?

**A:** Recall that the equation for slope is:

You have two points, (0,3) and (4,5), so you have (x1,y1) and (x2,y2). Put them into the formula:

m = (5-3) / (4-0)

m = 2 / 4

m = 1/2

So the slope is 1/2. This means it goes up 1, right 2.

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**Q:** Please show me how to write an equation that is the slope-intercept form of the equation of the line that passes through (1,2) and is parallel to 4x-2y=6

**A:** This looks hard at first, but it’s actually not too bad.

First, let’s rearrange the 4x-2y=6 line so that it’s in slope-intercept form, **y=mx+b**

4x-2y=6

4x-6=2y

Divide both sides by 2:

4x/2 -6/2 = y

2x – 3 = y

y=2x -3

So the slope of this line is 2, because m=2.

If a line is parallel to it, it must have the exact same slope. **Parallel lines always have identical slopes.** We know that this second line passes through the point (1,2), which means that x=1 and y=2. We already know that m=2, so put it all into the equation of a line and solve for b:

y=mx+b

2=2(1)+b

2=2+b

2-2=b

b=0

So the y-intercept is zero.

The equation of the line is:

**y=2x**

To see a graph of this line on Wolfram Alpha, click here.

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