Answer: Part A: y = x + 6
Part B: y = 10
The attachment shows the graphs of these equations.
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.