Question

A line passes through (4, 5) and (8, 9). Which equation best represents the line? y = x 1 y = 1 y = 2x 1 y = 5x 8.

Answer 1

Answer:

y = x + 1

Step-by-step explanation:

y = mx + b

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

m = $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

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

~~~~~~~~~~~~~

( 4 , 5 )

( 8 , 9 )

m = $\frac{9-5}{8-4}$ = 1

y - 5 = 1 ( x - 4 )

y = x + 1

Answer 2

The correct option is A, y=x+1.

a.) y = x+1

b.) y = 1

c.) y = 2x+1

d.) y = 5x+8.

Given to us,

$x_1=4\\y_1=5\\x_2=8\\y_2=9$

There are two ways to find the solution of such problems:

Case 1:

We know that for a line $y = mx + b$, where $m= \dfrac{rise}{run}= \dfrac{y_2-y_1}{x_2-x_1}$  therefore,

Value of slope, $m=\dfrac{rise}{run}= \dfrac{y_2-y_1}{x_2-x_1}=\dfrac{9-5}{8-4}=\dfrac{4}{4}=1$,

Now, substituting the value of slope in line equation,

$y=mx+b\\y=1\times x+b\\y=x+b$

Therefore, the answer should be option where variable x should not have any number with it.

Hence, the only option available is y = x+1.

Case II:

We can put the equations on graph as given in the picture,

y = x+1 (black line)

y = 1 (red line)

y = 2x+1 (blue line)

y = 5x+8 (green line)

See the image attached,

As there is only black line(y =x+1) passes through the point option A is the correct option.

 

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