Question

11c) Find the values for a and b.

Answer 1

Answer:

Part 11a) The slope of the line is $m=2$

Part 11b) The equation of the line is $y=2x-3$

Part 11c) The value of a is 7 and the value of b is 7

Part 11d) The y-coordinate is -1

Step-by-step explanation:

Part 11a) Find the slope of the line

we know that

we know that

The formula to calculate the slope between two points is equal to

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

take two points from the graph

(3,3) and (8,13)

substitute

$m=\frac{13-3}{8-3}$

$m=\frac{10}{5}$

$m=2$

Part 11b) Write the equation for the line

step 1

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=2$

$point\ (3,3)$

substitute

$y-3=2(x-3)$

step 2

Convert to slope intercept form

$y=mx+b$

isolate the variable y

$y-3=2(x-3)\\y-3=2x-6\\y=2x-6+3\\y=2x-3$

Part 11c) Find the values for a and b

step 1

Find the value of a

we have the ordered pair (5,a)

so

x=5, y=a

substitute the value of x in the linear equation and solve for y

$y=2(5)-3=7$

so

The value of a is 7

step 2

Find the value of b

we have the ordered pair (b,11)

so

x=b, y=11

substitute the value of y in the linear equation and solve for x

$11=2x-3\\2x=11+3\\2x=14\\x=7$

so

The value of b is 7

Part 11d) What is the y-coordinate when the x-coordinate is 1?

For x=1

substitute in the linear equation

$y=2(1)-3\\y=-1$

therefore

The y-coordinate is -1