Find the equations of the line that: A: Passes through the point (1,7) and (4,10)
B: Passes through the point (-2,10) and (4,10)

 Part A:  y = x + 6

Part B:  y = 10

The attachment shows the graphs of these equations.

Step-by-step explanation:

Find the slope, and then the y-intercept. Then write the equation in  Slope-intercept form . y= mx+b

m is the slope. b is the constant, the y-intercept.

First find the slope:  rise/run  

Rise is the difference in y-values  10-7 = 3

Run is the difference between x-values  4 - 1 = 3

The Slope is 3/3   simplify:

m = 1

Use this calculated slope with values of y and x from either of the given coordinates and calculate b

y = mx + b

10 = 1(4) + b  The 1 is not necessary, its "implied" and invisible as a factor in multiplication

10 = 4 + b .  subtract 4 from both sides  10 - 4 = 4 - 4  + b

6 = b

Put these calculated values for m and b into the slope-intercept equation"

y = x + 6

_________

Part B: Step-by-step explanation:  Slope-intercept form . y= mx+b

First find the slope:  rise/run  

Rise is the difference in y-values  10 - 10 = 0

At this point you know that if the slope is 0, it is a horizontal line intersecting the y-axis at the y-value, 10

That graphed line will pass through All x-values.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,