**Section 1-3**

(6) Graph y = x/2 +1. To find the x-intercept, set y = 0: To find the y-intercept, set x = 0: Thus the graph has x-intercept -2 and y-intercept 1 (see sketch). |

(8) Graph 8x - 3y = 24 To find the x-intercept, set y = 0: To find the y-intercept, set x = 0: Thus the graph has x-intercept 3 and y-intercept -8. It's sketched to the right. |

(10) y = 1/2 x + 1

This is of form y = mx + b, so we can instantly read off **slope = 1/2**
and **y-intercept is 1**

(14) Write the formula for a line with slope -2/3 and y-intercept -2. This
is kind of like the previous problem in reverse. Plugging this information into
the form y = mx + b, we get **y = -2/3 x - 2.**

(26) Find the slope and y-intercept of the line 3x - 2y = 10. To solve this problem we will put the equation into the form y = mx + b and read off the information.

3x - 2y = 10

-2y = -3x + 10

(-1/2)(-2y) = (-1/2)(-3x + 10)

y = 3/2 x - 5

Thus the **slope is 3/2,** and the **y-intercept is -5**

(34) Write the equation of the line with slope m = -2, and which passes through the point ( -3, 2).

**METHOD 1: **Use the point-slope formula y - y1 = m(x - x1)

y - 2 = -2(x - (-3))

y - 2 = -2x - 6

**y = -2x - 4**

**METHOD 2: **The equation will have the form y = mx +b, or rather y = -2x
+ b. To find b, plug (-3,2) into this equution and solve for b:

2 = -2(-3) + b

2= 6 + b

b = -4

Now that you know b, the equation is **y = -2x - 4.**

(40) Find the slope of the line passing through the points (2,1) and (10,5).
m = (5 - 1)/(10 - 2) = 4/8 = **1/2**

(50) Write an equation for the line passing through the points (3,7) and (-6,4).
The slope is m = (4 - 7)/(-6 - 3) = -3/-9 = 1/3.

Now, using the point-slope form, we get:

y - 7 = 1/3(x - 3)

y - 7 = 1/3 x - 1

-1/3 x + y = 6

-3( 1/3 x + y) = -3(6)

**x - 3y = -18**