The y-intercept of the line graph shown above is the value of the point where the line cuts the y-axis. The y-intercept of this graph is between 5 and 6. However, we can get an accurate value by calculation. This can be done by generating an equation of the line.

Recall the slope-intercept equation, $y = mx + b$ , where m = slope of the line, b = y-intercept.

To generate the equation of the line, first find slope using the points (-2, 7) and (6, 1):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 7}{6 -(-2)} = \frac{-6}{8} = -\frac{3}{4}$ .

Substitute m = ¾ and the coordinates (6, 1) into the slope-intercept equation to find the y-intercept (b):

$y = mx + b$

$1 = -\frac{3}{4}(6) + b$

$1 = -\frac{18}{4} + b$

$1 = -4.5 + b + 4.5$

$1 + 4.5 = -4.5 + b + 4.5$

$5.5 = b$

Therefore, b = y-intercept = 5.5.

To generate the equation of the line, plug in the values of m and b, we would have:

y = ¾x + 5.5

The y-intercept of the line of the graph is 5.5.

5 0

3 years ago

Describe what each transformation does to pre image to create its image

Kamila [148]

A rotation rotates the pre image an x amount of degrees
a translation shifts a pre image up and down or left and right
a reflection reflects an image across an x or
y axis
a dilation stretches or compresses(shrinks) a pre image

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3 years ago

Is the square root of 48 rational or irrational?

Dmitrij [34]

Square root of 48= Square root of 16 times 3= 4 Square root of three. The square root of 48 is an irrational number!

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Clara found the product of 3 – 6y2 and y2 + 2. Her work is shown below. (3 – 6y2)(y2 + 2) = 3(y2) + (–6y2)(2) = 3y2 – 12y2

Marizza181 [45]

<span>No, she did not use the distributive property correctly.</span>

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3 years ago

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