Mathematics, 11.12.2020 02:10 sassycutie523

Write an equation of line that passes through the points (4,3) land (1, 2) in point-slope form.

Answers: 3

Show answers

Answers

Answer from: anaroles04

$y=\frac{1}{3} x+\frac{5}{3}$

Step-by-step explanation:

Use the slope formula to find the slope:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}$

Insert the values:

$(4_{x_{1}},3_{y_{1}})\\\\(1_{x_{2}},2_{y_{2}})\\\\\frac{2-3}{1-4}=\frac{-1}{-3}=\frac{1}{3}$

The slope is 1/3.

You can do this two ways. You can solve using slope-intercept and solve for b, or use point-slope form, then simplify to slope-intercept

Use the slope-intercept form:

y=mx+b

where:

m is the slopeb is the y-interceptx and y are corresponding coordinate points (x,y)

Insert the slope and one of the given coordinate points:

$(1_{x},2_{y})\\\\2=\frac{1}{3} (1)+b$

Solve for the y-intercept. Simplify:

$2=\frac{1}{3} +b$

Subtract 1/3 from both sides:

$2-\frac{1}{3} =\frac{1}{3} -\frac{1}{3} +b\\\\2-\frac{1}{3} =b$

Subtract. Find the common denominator:

$\frac{6}{3} -\frac{1}{3} =\frac{5}{3}$

Insert:

$\frac{5}{3} =b$

The y-intercept is 5/3. Insert:

$y=\frac{1}{3}x+\frac{5}{3}$

Use point-slope form:

$y-y_{1}=m(x-x_{1})$

where:

m is the slopex1 and y1 are corresponding coordinate points

Insert values:

$(1_{x_{1}},2_{y_{1}})\\\\y-2=\frac{1}{3} (x-1)$

Simplify the equation by solving for y. This will result in the slope-intercept form. Simplify multiplication using the rule $\frac{a}{b} *c=\frac{ac}{b}$ :

$y-2=\frac{1(x-1)}{3} \\\\y-2=\frac{x-1}{3}$

Isolate the variable. Add 2 to both sides:

$y-2+2=\frac{x-1}{3} +2\\\\y=\frac{x-1}{3}+2$

Simplify to slope-intercept form, y=mx+b. Use the rule $\frac{a-b}{c} =\frac{a}{c}-\frac{b}{c}$ :

$y=\frac{x}{3} -\frac{1}{3} +2$

Combine like terms. Find a common denominator:

$-\frac{1}{3}+2=-\frac{1}{3}+\frac{2}{1}\\\\-\frac{1}{3}+\frac{3*2}{3*1}=-\frac{1}{3}+\frac{6}{3} \\\\-\frac{1}{3}+\frac{6}{3} =\frac{5}{3}$

Insert:

$y=\frac{x}{3} +\frac{5}{3}$

Use the rule $\frac{x}{a} =\frac{1}{a}x$ :

$y=\frac{1}{3} x+\frac{5}{3}$

:Done

Answer from: Quest

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

the function given is y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 = -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24

Answer from: Quest

step-by-step explanation:

the answer is a