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None of the given options are matching. For the expression after putting the value 2 on the place of x. We will get 10 for expression 1 and 0 for the expression 2.
<h3>How can we find the solution to an equation?</h3>
We do same operations on both the sides so that equality of both expressions doesn't get disturbed.
Solving equations generally means finding the values of the variables used in it for which the considered equation is true.
The given equation is;
Equation 1;
Equation 2;
After putting the value 2 on the place of x we get;
Equation 1;
Equation 2;
Hence, the none of the given options are matching.
To learn more about the equation, refer to the link;
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Answer:
A. Please see the attached graphs
B. 5. The equation of the graph is y = 3·x - 3
6. The equation of the graph is y = x + 3
7. The equation of the graph is y = 4/5·x - 4
8. The equation of the graph is y = 2·x - 4
9. The graph is the line with equation y = 5·x - 31
10. The graph is the line with equation y = 5·x - 14
11. The graph is the line with equation y = -2·x + 9
12. The graph is the line with equation y = 3·x + 6
Step-by-step explanation:
A. Please see the attached graphs
B. 5. The intercepts are;
(0, -3) and (1, 0)
The slope is given by the following equation;
For the coordinate points, (0, -3) and (1, 0) we have;
m = (0 - (-3))/(1 - 0) = 3
The slope = 3
From the point and slope form, of a straight line equation, we have;
y - 0 = 3(x - 1)
The equation of the graph is therefore;
y = 3·x - 3
The y-intercept occurs at (0, -3)
The x intercept occurs where y = 0
0 = 3·x - 3
x = 3/3 = 1
The x-intercept occurs at (1, 0)
The graph of the equation, y = 3·x - 3, passes through the y and x intercepts (0, -3) and (1, 0) respectively
6. The coordinate points are;
(-3, 0) and (0, -3)
The slope is given by the following equation;
For the coordinate points, (-3, 0) and (0, -3) we have;
m = ((-3) - 0)/(0 - (-3)) = -1
The slope = 1
From the point and slope form, of a straight line equation, we have;
y - 0 = 1(x - (-3)) = x + 3
y = x + 3
The y-intercept occurs at (0, 3)
The x intercept occurs where y = 0
0 = x + 3
x = -3
The x-intercept occurs at (-3, 0)
The graph of the equation, y = x + 3, passes through the y and x intercepts (0, 3) and (-3, 0) respectively
7. The coordinate points are;
(5, 0) and (0, -4)
The slope is given by the following equation;
For the coordinate points, (5, 0) and (0, -4) we have;
m = ((-4) - 0)/(0 - 5) = 4/5
The slope = 4/5
From the point and slope form, of a straight line equation, we have;
y - 0 = 4/5×(x - 5) = -4/5·x - 4
y = 4/5·x - 4
The y-intercept occurs at (0, -4)
The x intercept occurs where y = 0
0 = -4/5·x + 4
-4 = -4/5·x
x = 5
The x-intercept occurs at (5, 0)
The graph of the equation, y = 4/5·x - 4, passes through the y and x intercept (0, 4) and (5, 0) respectively
8. The coordinate points are;
(2, 0) and (0, -4)
The slope is given by the following equation;
For the coordinate points, (2, 0) and (0, -4) we have;
m = ((-4) - 0)/(0 - 2) = 2
The slope =2
From the point and slope form, of a straight line equation, we have;
y - 0 = 2×(x - 2) = 2·x - 4
y = 2·x - 4
The y-intercept occurs at (0, -4)
The x intercept occurs where y = 0
0 = 2·x - 4
4 = 2·x
x = 2
The x-intercept occurs at (2, 0)
The graph of the equation, y = 2·x - 4 passes through the y and x intercept (0, -4) and (2, 0) respectively
C. Using the point and slope form
9. The slope m = 5 and the graph passes through the points (6, -1)
We have the point and slope form given as follows;
y - (-1) = 5·(x - 6)
y = 5·x - 30 - 1 = 5·x - 31
y = 5·x - 31
The graph is the line with equation y = 5·x - 31
10. The slope m = 5 and the graph passes through the points (2, -4)
We have the point and slope form given as follows;
y - (-4) = 5·(x - 2)
y = 5·x - 10 - 4 = 5·x - 14
y = 5·x - 14
The graph is the line with equation y = 5·x - 14
11. The slope m = -2 and the graph passes through the points (4, 1)
We have the point and slope form given as follows;
y - 1 = (-2)·(x - 4)
y = -2·x + 8 + 1 = -2·x + 9
y = -2·x + 9
The graph is the line with equation y = -2·x + 9
12. The slope m = 3 and the graph passes through the points (-3, -3)
We have the point and slope form given as follows;
y - (-3) = 3·(x - (-3))
y = 3·x + 9 - 3 = 3·x + 6
y = 3·x + 6
The graph is the line with equation y = 3·x + 6
