Sarah compared the function y = 7x + 13to the linear function that fits the valuesin the table below. what is the distancebetween the y-interceptsof the two functions? x. y-3. 12. -95. -157. -19a) 5b) 9c) 13d) 18

d) 18

Step-by-step explanation:

The question is on graphing linear functions

Given the table of values of x and y, plot the graph and observe the gradient of -2 and the y-intercept at (0,-5) as shown on the attached graph with blue color.

Use the given function y=7x+13 to formulate a table of values of x with corresponding values of y

x     y

-3   -8

0      13

1       20

With the above values, plot the graph of y=7x+13 and obtain the y-intercept at (0,13) as shown in the red line graph attached.

To find the distance between the y-intercepts of the two graphs we apply the expression for distance between two points;

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points are (0,-5) and (0,13)

D=√ (0-0)² + (13--5)²

D=√(18)²

D=18 units

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.