Use the image to answer the question. Use the graph to derive the equation of the line in slope-intercept form. (1 point)
To find the equation of the line in slope-intercept form, we first need to determine the slope and the y-intercept from the graph.
The slope is the change in y divided by the change in x between two points on the line. We can choose two points on the line and calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's choose the points (0, 12) and (4, 4) on the line:
slope = (4 - 12) / (4 - 0)
slope = -8 / 4
slope = -2
So, the slope of the line is -2.
Next, we need to find the y-intercept, which is the value of y when x = 0. From the graph, we can see that the y-intercept is 12.
Now we can write the equation of the line in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. So, substituting m = -2 and b = 12, we get:
y = -2x + 12
Therefore, the equation of the line in slope-intercept form is y = -2x + 12.
(0,-2) (1,3)
To find the equation of the line in slope-intercept form using the points (0, -2) and (1, 3), we first need to calculate the slope using the formula:
m = (y2 - y1) / (x2 - x1)
Substitute the coordinates (0, -2) and (1, 3) into the formula:
m = (3 - (-2)) / (1 - 0)
m = (3 + 2) / 1
m = 5
So, the slope of the line is 5.
Next, we can use the point-slope form of the equation of a line:
y = mx + b
Where m is the slope and (x, y) is a point on the line. We can substitute the slope m=5 and point (1, 3) into the equation:
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Thus, the y-intercept is -2.
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 2
Use the table to answer the question. x y −5 0 0 5 2 7 Which linear equation represents this nonproportional linear relationship? (1 point) Responses y=15x+5 y equals Start Fraction 1 over 5 End Fraction x plus 5 y=−5x+5 y equals negative 5 x plus 5 y=−x+5 y equals negative x plus 5 y=x+5
To find the linear equation representing the nonproportional linear relationship given in the table, we can first calculate the slope by choosing two points from the table.
Let's choose the points (0, 5) and (2, 7) for the calculation:
Slope (m) = (y2 - y1) / (x2 - x1)
m = (7 - 5) / (2 - 0)
m = 2 / 2
m = 1
So, the slope of the line is 1.
Now that we have the slope, we can use the point-slope form of a linear equation (y = mx + b) and substitute one of the points, for example, (0, 5) to find the y-intercept (b).
5 = 1(0) + b
b = 5
Therefore, the y-intercept is 5.
So, the linear equation that represents this nonproportional linear relationship is:
y = x + 5
Write y−6x=5 in slope-intercept form(1 point) y=
To write the equation y - 6x = 5 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we need to solve for y by isolating it on one side of the equation.
Add 6x to both sides of the equation:
y - 6x + 6x = 5 + 6x
y = 6x + 5
Therefore, the equation y - 6x = 5 in slope-intercept form is:
y = 6x + 5
Describe what makes a proportion. Give an example of a proportion.(2 points)
A proportion is an equation that states two ratios are equal. In a proportion, the two ratios are set equal to each other, and they can be simplified to the same value. In other words, a proportion is a statement that two ratios are equivalent.
For example, consider the proportion:
3/4 = 6/8
This proportion states that the ratio of 3 to 4 is equal to the ratio of 6 to 8. We can simplify this proportion by cross-multiplying:
3 * 8 = 24
4 * 6 = 24
Thus, the proportion 3/4 = 6/8 is true because both sides simplify to the same value of 3/4. This example illustrates the concept of proportions, where two ratios are equal to each other.