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