Explain how to find the slope of a line that passes through the points (-3, 1), (1, 9. Find the slope
1 answer:
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Answer:
The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is
Step-by-step explanation:
We need to Write the equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x
The equation in slope-intercept form is: where m is slope and b is y-intercept.
Finding Slope:
The both equations given are parallel. So, they have same slope.
Slope of given equation y= - 2/3x is m = -2/3
This equation is in slope-intercept form, comparing with general equation where m is slope , we get the value of m= -2/3
So, slope of required line is: m = -2/3
Finding y-intercept
Using slope m = -2/3 and point (-3,5) we can find y-intercept
So, we get b = 3
Now, the equation of required line:
having slope m = -2/3 and y-intercept b =3
The equation of the line in slope intercept form that passes through the point (-3, 5) and is parallel to y= - 2/3x is
Answer: The correct option are as follows;
(1) The triangles are similar because corresponding sides are congruent
(2) The triangles are similar because alternate interior angles are congruent
(3) In the similar triangles, Angle 3 and Angle 6 are corresponding angles
Step-by-step explanation: Please refer to the picture attached for details.
The line i and line e has been drawn and marked as parallel lines. Also two transversal lines m and n have been drawn to intersect in the region between the parallel lines to form two triangles (as shown in the picture).
From the information given, where line e intersects with line n we have angle 1, and where line e intersects with line m we have angle 3, and then the third angle is angle 2.
Furthermore, where line l intersects line m we have angle 6, and where line l intersects line n is angle 4. Also in this second triangle, the third angle is 5.
Upon close observation we would see that Angle 6 is equal to Angle 3, since the transversal m has cut across both parallel lines l and e. Similarly Angle 4 is equal to Angle 1 since the transversal n has cut across parallel lines l and e. Having that Angles 3 and 1 are congruent to Angles 6 and 4, we can conclude that the value of the third angle in one triangle is equal to the that of the third in the second triangle, that is, Angle 2 equals Angle 5. Also, if the angles are similar and the lines l and e are parallel, then the lines formed in both triangles are equal.
So our conclusions are;
The interior angle are alternate angles (Angles 3 and 6, Angles 1 and 4), and the third interior angles are Opposite (Angles 2 and 5 {Opposite angles are equal})
