Answer:
(d) y = 3/4x +1/2
Explanation:
You want the equation representing the line shown in the graph.
Slope-intercept equation
The line is shown between points A(-2, -1) and B(6, 5). The slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (5 -(-1))/(6 -(-2)) = 6/8 = 3/4
The y-intercept can be found using the formula ...
b = y1 -m(x1)
b = -1 -(3/4)(-2) = 1/2
Then the slope-intercept equation is ...
y = mx +b
y = 3/4x +1/2
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Additional comment
The line crosses the y-axis between y=0 and y=1, so you know the y-intercept is positive. This eliminates answer choices A and C.
The y-value of 5 corresponding to the x-value of 6 (at point B) tells you the slope of the line is less than 5/6. This eliminates answer choices A and B.
The only viable answer choice is D, which is the correct one.
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