5) Allison plays a card game. She picks a card at random. Then without putting

Y-8= - * - 4 y=-* 4 (3,-5) no solution an infinite number of solutions

muminat

Given:

The system of equation is

$y-8=-\dfrac{1}{3}x-4$

$y=-\dfrac{1}{3}x-4$

To find:

The solution of given system of equations.

Solution:

The slope intercept form of a line is

$y=mx+b$

Where, m is slope and b is y-intercept.

Write the given equation in slope intercept form.

The first equation is

$y-8=-\dfrac{1}{3}x-4$

$y=-\dfrac{1}{3}x-4+8$

$y=-\dfrac{1}{3}x+4$ ...(i)

Here, slope is $-\dfrac{1}{3}$ and y-intercept is 4.

The second equation is

$y=-\dfrac{1}{3}x-4$ ...(i)

Here, slope is $-\dfrac{1}{3}$ and y-intercept is -4.

Since the slopes of both lines are same but the y-intercepts are different, therefore the given equations represent parallel lines.

Parallel lines never intersect each other. So, the given system of equation has no solution.

Hence, the correct option is B.

3 0

3 years ago

A line passes through the points (7, 10) and (7, 20). Which statement is true about the line? It has a slope of zero because x 2

yaroslaw [1]

Answer:

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

Step-by-step explanation:

Points:

(7, 10) and (7, 20)

Slope-intercept form:

y= mx+b

slope is:

m= (y2-y1)/(x2-x1)= (20-10)/(7-7)= 10/0,

denominator of the fraction is zero, we can't divide by zero, so this line has no slope

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It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

no, numerator is not zero

It has a slope of zero because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.

no, it has no slope

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the numerator of a fraction cannot be zero.

no, numerator is not zero

It has no slope because x 2 minus x 1 in the formula m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction is zero, and the denominator of a fraction cannot be zero.