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.
Answers
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.
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Answers
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Step-by-step explanation:
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i just took the quiz, it’s 25.
What is the equation of the line that passes through the point (−3,4) and has a slope of 1 ?
Answers
Answer:
y = x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 1, thus
y = x + c ← is the partial equation
To find c substitute (- 3, 4) into the partial equation
4 = - 3 + c ⇒ c = 4 + 3 = 7
y = x + 7 ← equation of line
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We have following equation to find the point-slope form of the linear functions.
[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]
[tex]m = slope = 1[/tex]
Now just need to put the coordinates and the slope in the above equation.
[tex]y - 4 = 1 \times ( \: x - ( - 3) \: )[/tex]
[tex]y - 4 = x + 3[/tex]
Add sides 4
[tex]y - 4 + 4 = x + 3 + 4[/tex]
[tex]y = x + 7[/tex]
Done...
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Answers
Answer:
x=-2
Step-by-step explanation:
The line is vertical and/or undefined and it passes through the point (-2,5).
2x+y =8 and y=x-7 solve by substitution
Answers
Answer:
you can do this by this please vote also
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Answers
Answer:
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Step-by-step explanation:
[tex]\frac{11}{12} *\frac{4}{5}[/tex]
You can simplify to make life easier
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Answer:
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Step-by-step explanation:
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Answers
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Answers
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Answers
Answer:
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Answer:
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Step-by-step explanation:
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PLEASE AND THANKSSS:))
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
PLEASE HELP ME I REALLY NEED HELP IN ALGEBRA
(a) Does the graph represent a constant-rate relationship?
(b) Explain how you determined your answer in part A.
(c) If this is a constant-rate relationship, what is the constant rate?
Answers
Answer:
A no it is not
B his is because if you look at 1 on the x axis line you will see it matches 1 on the y axis but if you look at 4 on the x axis it is 2 on the y axis so it is not constant
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WILL PAY 40 POINTS AND BRAINLIEST!!!!
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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Answers
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Answers
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Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
have a nice rest of your day
PLEASE ANSWER BRAINIEST
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Step-by-step explanation:
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Determine the intercepts of the line.
x-intercept(_,_)
y-intercept(_,_)
Answers
Answer:
the X - intercept is (-7,0)
the Y - intercept is (0,2)
Step-by-step explanation:
the Y intercept is where the line crosses the Y axis
the X intercept is where the line crosses the X axis
Hope this helps
Find the slope of the line that passes through (-3,4) and (-2,-8)
Answers
Answer:
-12
Step-by-step explanation:
The slope formula is y2-y1 divided by x2-x1
I plugged it in and got
-12
I hope this helps :>