**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
**only one** has a slope (m) = 5

• There are **several** forms for the equation that represents such a line. Let’s consider
**only two** of them: **slope intercept** form and
**point slope** form.

**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

• **Point Slope** Form equation:** 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 **Slope Intercept** Form equation:** 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 **slope intercept equation is a true equation** for our line!

**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!

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

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).

**Remember**: RISE = change of “y”

**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!