Section 1-3

(6) Graph y = x/2 +1. This is of the form y = mx + b (with m = 1/2) so the graph will be a straight line. To find the x-intercept, set y = 0: 0 = x/2 +1 -x/2 = 1 -2(-x/2) = -2(1) x = -2 To find the y-intercept, set x = 0: y = 0/2 + 1 y = 1 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: 8x -3(0) = 24 8x = 24 x = 3. To find the y-intercept, set x = 0: 8(0) -3y = 24 -3y = 24 y = -8 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