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andreyandreev [35.5K]
2 years ago
12

11c) Find the values for a and b.

Mathematics
1 answer:
Luba_88 [7]2 years ago
5 0

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

<em>step 1</em>

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)

<em>step 2</em>

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

<em>step 1</em>

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

<em>step 2 </em>

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

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