The graph of linear function k passes through the points(-7,0) and (1,8). Which statement must be true
Answers
The slope of the graph of k is -4/3.
The graph of k passes through the point (-1,-8).
The zero of k is 7
The x-intercept of the graph of k is -7.

The Graph Of Linear Function K Passes Through The Points(-7,0) And (1,8). Which Statement Must Be TrueAnswers

Answers

Answer 1

Answer:

✅The x-intercept of the graph of k is -7.

Step-by-sep explanation:

Graph the equation of the line that passes through the points, (-7, 0) and (1, 8) by first generating an equation, and then using the equation of the function to plot the graph.

To find the equation, we need to calculate the slope, m, and y-intercept, b.

✅Using points (-7, 0) and (1, 8), the slope of the line is:

[tex] m = \frac{y_2 - y_1}{x_2 -x_1} = \frac{8 - 0}{1 -(-7)} = \frac{8}{8} = 1 [/tex]

Substitute x = 1, y = 8, m = 1 into [tex] f(x) = mx + b [/tex] to find the y-intercept, b, of the function. (Note: f(x) is same as variable y).

[tex] 8 = 1(1) + b [/tex]

[tex] 8 = 1 + b [/tex]

Subtract 1 from each side

[tex] 8 - 1 = b [/tex]

[tex] 7 = b [/tex]

[tex] b = 7 [/tex]

Substitute m = 1 and b = 7 into [tex] f(x) = mx + b [/tex]

The equation of the function is:

[tex] f(x) = (1)x + 7 [/tex]

[tex] f(x) = x + 7 [/tex]

The graph of the function, k, is shown in the attachment below.

❌Now, we know that the slope of the function, m, is 1. Therefore, option A is not correct.

We also know that the graph of the function, k, does not pass through the points (-1, -8). We can confirm this looking at the graph. ❌The point (-1, -8) is not on the line of the graph. Therefore, option B is not correct.

❌The zero of k, is the value of x for which the function, f(x) or y = 0. From our graph, y = 0, when x = -7. This can also be referred to as the x-intercept. The zero of k is -7, not 7.

Therefore, option C is not correct.

✅The x-intercept is where the line of the function of intercepts the x-axis. From our graph, the line intercepts the x-axis at x = -7.

So, the x-intercept of the graph of k is -7.

Therefore, option D is the only statement that is TRUE.

The Graph Of Linear Function K Passes Through The Points(-7,0) And (1,8). Which Statement Must Be TrueAnswers

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A line goes through the points (-3 1) and (-2 4)
(a) What is the slope of the line? Show your work.
(b) Write the equation of the line in point-slope form. Show your work.
(c) Write the equation of the line in slope-intercept form. Show your work.

Answers

Answer:

Part A)

The slope is 3.

Part B)

[tex]\displaystyle y-1=3(x+3)[/tex]

Part C)

[tex]\displaystyle y=3x+10[/tex]

Step-by-step explanation:

We know that the line goes through the points (-3, 1) and (-2, 4).

Part A)

To find the slope of a line given two points, we can use the slope formula:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where (x₁, y₁) and (x₂, y₂) are our two points.

So, let’s let (-3, 1) be (x₁, y₁) and let (-2, 4) be (x₂, y₂). Substitute appropriately:

[tex]\displaystyle m=\frac{4-1}{-2-(-3)}[/tex]

Evaluate:

[tex]\displaystyle m=\frac{3}{-2+3}=\frac{3}{1}=3[/tex]

Hence, the slope of our line is 3.

Part B)

Point-slope form is given by:

[tex]\displaystyle y-y_1=m(x-x_1)[/tex]

Where m is our slope and (x₁, y₁) is a point.

So, let’s substitute 3 for m.

For our point, we can use either of the two given. Let’s use (-3, 1) for consistency. So, let (-3, 1) be (x₁, y₁). Therefore:

[tex]\displaystyle y-1=3(x-(-3))[/tex]

Simplify. Hence, our point-slope form is:

[tex]\displaystyle y-1=3(x+3)[/tex]

Part C)

To rewrite into slope-intercept form, we can just solve for y from our point-slope form. So, we have:

[tex]\displaystyle y-1=3(x+3)[/tex]

Distribute on the right:

[tex]\displaystyle y-1=3x+9[/tex]

Add 1 to boths sides. So, our slope-intercept equation is:

[tex]\displaystyle y=3x+10[/tex]

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Step-by-step explanation:

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[tex]y - y(0) = m \times ( \: x - x(0) \:) [/tex]

In which :

[tex]y(0) = y \: \: given \: \: point = 4[/tex]

[tex]x(0) = x \: \: given \: \: point = - 3[/tex]

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