Answer:
1. D. 2x + y = 4
2. A
Explanation:
Problem 1:
To find the equation in standard form, first find the equation of the graph in slope-intercept form, y = mx + b.
Where, m = slope and b = y-intercept.
Slope (m) = ∆y/∆x
Using two points on the line, (0, 4) and (2, 0):
Slope (m) = (0 - 4)/(2 - 0) = -4/2 = -2
m = -2
y-intercept is the y-coordinate of the point where the line intercepts the y-axis = 4.
Thus,
b = 4
Substitute m = -2, and b = 4 into y = mx + b:
y = -2x + 4
Rewrite in standard form:
2x + y = 4
Problem 2:
The funtion y = ½(x) + 2 is given in the slope-intercept form y = mx + b.
m = slope = ½
b = y-intercept = 2
Therefore, the graph that has a slope value of ½ and y-intercept value of 2 would be the graph that represents the given function.
Thus, the graph in option A, has a y-intercept (b) value of 2 (the line intercepts the y-axis at y = 2).
Also, the slope of graph A = ½.
Therefore, the answer is option A.