Question

Find the equations of the line that:

Answer 1

Answer:  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.