Not sure what the answer is to this one

## the equation that represents the line that passes through the point (-2, -1) and has a slope of 5.

# 4 Answers

**Solution**:** y + 1 = 5 (x+2)**
* in point slope form or* **y = 5 x + 9 **

*in intercept slope form*

PLEASE READ FOLLOWING STEP BY STEP SOLUTION!

**STEP 1**: **
Read**, **understand** the situation within, **identify** and pull out
**important** **information**.

• There are * infinite* lines passing through the point (-2,-1), but

*has a slope (m) = 5*

**only one**• There are

*forms for the equation that represents such a line. Let’s consider*

**several***of them:*

**only two***form and*

**slope intercept***form.*

**point slope****STEP 2**: **
Translate** each of the **keywords** in the problem to their mathematical symbols.

• * Slope Intercept* Form equation:

**y = mx + b**; m = slope; b = y-intercept

•

*Form equation:*

**Point Slope****y – y1 = m (x – x1)**; m = slope; (x1, y1) are the coordinates of the given point (-2,-1).

**STEP 3**: **Set up** and
**solve** the equation:

• * Point Slope Form equation*: y – y1 = m (x – x1); where m = slope; (x1, y1) = (-2,-1)

y – (-1) = 5 (x – (-2)) by substituting the coordinates of the given point

**y + 1 = 5 (x+2)**; This is the “point slope form equation” representing the line.

• * Slope Intercept Form equation*:

y = 5 x + b ; substituting m = 5

-1 = 5 (-2) + b ; substituting the coordinates of the point (-2,-1) to determine b

-1 = -10 + b;

b = 10 – 1 ;

b = 9

**y-intercept****y = 5 x + 9**this is the slope intercept form equation that represents the line through (-2,-1) with the slope of 5.

**STEP 4**: **
Verify** your answer.

• In the * Point Slope* Form:

**y + 1 = 5 (x+2)**

y + 1 = 5x + 10 by applying the Distributive Property of Multiplication

y1 + 1 = 5x1 + 10 now substitute the coordinates (x1, y1) of the given point (-2, -1)

-1 + 1 = 5*(-2) + 10

0 = -10 +10

0 = 0 This is an identity!, so our point slope equation is a true equation for our line!

• In the

*Form equation:*

**Slope Intercept****y = 5x + 9**

y1 = 5x1 + 9 by substituting the coordinates (x1,y1) of the given point (-2,-1)

-1 = 5*(-2) + 9

-1 = -10 + 9

-1 = -1

*This is an identity!*Our

*for our line!*

**slope intercept equation is a true equation****STEP 5**: **
Curiosities**

• The * slope intercept form* is a

*:*

**particular case of the point slope form**y + 1 = 5x + 10 point slope form

y = 5x + 9 by isolating “y”, we get the slope intercept form!

•

*the line through (-2, -1) with the slope of 5:*

**Graphing**m = RISE / RUN ;

m = 5 ; The slope is positive, so it’s upward going from left to right.

m = 5/1;

RISE = 5; RUN = 1.

Plot the given point (-2,-1) on a Cartesian plane. Starting on this point go up 5 units (RISE =5), and then to the right 1 unit (RUN = 1). You get the point (-1,4).

*: RISE = change of “y”*

**Remember****RISE = y2 – y1**; so,

y2 = RISE + y1

y2 = 5 + (-1) ;

**y2 = 4**this is the y-coordinate of the second point!

Do the same for the RUN and you get x2 = RUN – x1

x2 = 1 + (-2)

**x2 = -1**this is the x-coordinate of the second point.

So the

**second point is P2 = (-1,4)**.

Finally: draw a line connecting the two points (-2,-1) and (-1,4). There you go!

Hi -- For this problem, you have already been given some useful information and can use the information to plug in to the standard point-slope formula. When we talk about point-slope, we mean we have one point defined (-2,-1) and the slope is known (which is 5/1).

First, we have the point-slope formula:

y-y_{1} = m(x-x_{1})

Second, we will plug in what we know from what was given in the problem

x_{1} = -2 and y_{1} = -1

m = 5

Third, let's plug in what we know!

y-(-1) = 5(x-(-2)) Don't forget a (-)(-) = +

y+1 = 5(x+2) Now, distribute the 5 across (x+2)

y+1 = 5x+10 Now, combine like terms by subtracting 1 from both sides

y = 5x+9 This is the equation of your line with m=5 and y-intercept = (0,9)

For this you can use the classic slope-intercept formula:

y = mx + b

They give you a point with x and y coordinates and they give you the slope so you just have to solve for b (also known as the y-intercept):

-1 = (5*-2) + b

-1 = -10 + b

9 = b

Now you just use the values of m = 5 and b = 9 to rewrite the equation as:

y = 5x + 9

The point-slope formula for a line through (x_{0},y_{0}) and having slope m is:

y = m(x - x_{0}) + y_{0}

You can plug in the information x_{0} = -2, y_{0} = -1, m = 5 and simplify.

y = 5(x + 2) - 1

y = 5x + 10 - 1

y = 5x + 9