Question

points in the picture are on the same line. (4 pts.)a. Find the slope of the line. Explainуor show your reasoning.(5.13)b. Write an equation for the line.(c, 10)(2,4)c. What is the value of c? Explain orshow your reasoning.d. Is the point (0,-2) on this line?Explain how you know.

Answer 1

a .

Apply the slope formula (m)

$m=\text{ }\frac{y2-y1}{x2-x1}$

Use two points from the graph:

(x1,y1) = (2,4)

(x2,y2) = (5,13)

Replace in the formula:

$m=\frac{13-4}{5-2}$$m=\frac{9}{3}=3$

b. equation of the line:

y=mx+b

where:

m= slope

b= y-intercept

Replace (x,y) by a point from the graph, for example (2,4) and solve for b

4 = 3(2)+b

4=6+b

4-6 =b

-2=b

y= 3x-2

c. value of c

Replace the y coordinate (10) ans solve for x:

10= 3x-2

10+2=3x

12 =3x

12/3 = x

4=x

c=4

d. replace (0,2) in the equation and check if the equality remains:

y=3x-2

2 = 3(0)-2

2=-2

2 is not equal to -2.

So, (0,2) is no on this line.