Hi there! :)
Answer:
Given line with an equation of y = 4x + 3
Parallel lines contain equivalent slopes, so a parallel line to the given equation would contain a slope of m = 4.
Plug in the coordinates of the point given, along with the slope into the equation y = mx + b where:
m = slope
y = y-coordinate of point
x = x-coordinate of point
Solve for the 'b' value, or y-intercept:
y = mx + b
6 = 4(2) + b
6 = 8 + b
b = -2
Rewrite the equation as slope-intercept form:
y = 4x - 2
Answer:
A) Same shape
C) Similar
Step-by-step explanation:
The figure is missing: find it in attachment.
Here we want to compare the two triangles: Let's analyze each statement.
A) Same shape --> TRUE
In fact, we see that the 3 angles of the two triangles are the same: therefore, the two triangles have same shape.
B) Congruent --> FALSE
Two triangles are said to be congruent if they have same sizes and same angles: here we see that they do not have the same sizes, so they are not congruent.
C) Similar --> TRUE
Two triangles are said to be similar if the proportions between their sides are the same.
For the triangles in the figure, we see that this is valid. In fact, the ratio of the 3 sides for the triangle on the left is 10:8:6, while the ratio for the triangle on the right is 20:16:12, which can be reduced to 10:8:6: therefore, the same ratio.
D) Same size --> FALSE
As we see, the two triangles do not have the same size.
