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QuestionFind the slope and y-intercept for each line: 39. y=2x+1y=2x+1, 40. y=3x+2y=3x+2, 41. f(x)=−2x+1f(x)=-2x+1, 42. f(x)=−3x+2f(x)=-3x+2, 43. f(x)=34x−2f(x)=\frac{3}{4}x-2, 44. f(x)=34x−3f(x)=\frac{3}{4}x-3, 45. y=−35x+7y=-\frac{3}{5}x+7, 46. y=−25x+6y=-\frac{2}{5}x+6, 47. g(x)=−12xg(x)=-\frac{1}{2}x, 48. g(x)=−13xg(x)=-\frac{1}{3}x. Graph each function.

Studdy Solution

STEP 1

Assumptions1. The equations given are linear functions in the form of y=mx+by = mx + b or f(x)=mx+bf(x) = mx + b or g(x)=mxg(x) = mx, where m is the slope and b is the y-intercept. . The slope of a line is the change in y divided by the change in x.
3. The y-intercept is the y-coordinate where the line intersects the y-axis (i.e., where x =0).

STEP 2

For the equation y=2x+1y=2 x+1, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=2,b=1m =2, b =1

STEP 3

For the equation y=3x+2y=3 x+2, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=3,b=2m =3, b =2

STEP 4

For the equation f(x)=−2x+1f(x)=-2 x+1, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=−2,b=1m = -2, b =1

STEP 5

For the equation f(x)=−3x+2f(x)=-3 x+2, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=−3,b=2m = -3, b =2

STEP 6

For the equation f(x)=34x−2f(x)=\frac{3}{4} x-2, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=34,b=−2m = \frac{3}{4}, b = -2

STEP 7

For the equation f(x)=34x−3f(x)=\frac{3}{4} x-3, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=34,b=−3m = \frac{3}{4}, b = -3

STEP 8

For the equation y=−35x+7y=-\frac{3}{5} x+7, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=−35,b=7m = -\frac{3}{5}, b =7

STEP 9

For the equation y=−25x+6y=-\frac{2}{5} x+6, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=−25,b=6m = -\frac{2}{5}, b =6

STEP 10

For the equation g(x)=−2xg(x)=-\frac{}{2} x, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=−2,b=0m = -\frac{}{2}, b =0

STEP 11

For the equation g(x)=−3xg(x)=-\frac{}{3} x, the slope (m) is the coefficient of x, and the y-intercept (b) is the constant term.
m=−3,b=0m = -\frac{}{3}, b =0

STEP 12

To graph these functions, we start by plotting the y-intercept (b) on the y-axis. Then, from this point, we use the slope (m) to find another point on the line. The slope is the ratio of the vertical change (rise) to the horizontal change (run). For example, if the slope is2, we move2 units up for every unit we move to the right. If the slope is -2, we move2 units down for every unit we move to the right. If the slope is a fraction, like/4, we move units up for every4 units we move to the right. If the slope is a negative fraction, like -/4, we move units down for every4 units we move to the right.

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