Question

1-40.

A line passes through the points A-3, -2) and B(2, 1). Does it also pass through the point
C(5,3)? Justify your conclusion. 1-10 HW Jool (Desmos). Homework Help
I

Answer 1

To determine if the line passing through points A (-3, -2) and B (2, 1) also passes through point C (5, 3), we can calculate the slopes of both line AB and line AC.

Step-by-step explanation:

To determine if the line passing through points A (-3, -2) and B (2, 1) also passes through point C (5, 3), we can calculate the slopes of both line AB and line AC. If the slopes are equal, then the line passes through point C.

The slope of line AB can be calculated using the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates of points A and B, we get: slope_AB = (1 - (-2)) / (2 - (-3)) = 3/5.

Similarly, the slope of line AC is: slope_AC = (3 - (-2)) / (5 - (-3)) = 5/8.

Since the slopes of line AB and line AC are not equal, we can conclude that the line passing through points A (-3, -2) and B (2, 1) does not pass through point C (5, 3).

Answer 2

Answer: No it does not .

Step-by-step explanation:

First use the coordinates of point A and B to write an equation.

A (-3,-2)

B(2,1)

We will need to use these points to find the slope first and by doing that we will find the difference in the y values and divide it by the difference in the x values.

-2-1= -3

-3-2 = -5

-3/-5= 3/5

The slope is 3/5 and now we need to find the y intercept using the same points. As you can see the equation will have to be in slope intercept form which uses the formula y=mx+b where m is the slope and b is the y-intercept.

We will plot the first points in and solve for b.

-2=3/5(-3) + b

-2= -9/5 + b

+9/5 +9/5

b = -1/5

We will now write the equation y=3/5x - 1/5 .

Now using the equation try point c to see if it fits the graph.

Point C is (5,3) so again plot in the x and y coordinates and solve,

3= 3/5(5) - 1/5

3 = 3 - 1/5

3
`\\eq` 14/5

In this case 3 does not equal 14 over 5 so Point c does not fit the graph