Answer:
y = x + 1
Step-by-step explanation:
1) First, find the slope of the line between the two points. Whichever option has the same slope would be the right answer. To find this, use the slope formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]. [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point, and [tex]x_2[/tex] and [tex]y_2[/tex] represent the x and y values of another point.
So, use the points given to answer the question. Substitute 4 for [tex]x_1[/tex], 5 for [tex]y_1[/tex], 8 for [tex]x_2[/tex], and 9 for [tex]y_2[/tex] then solve:
[tex]\frac{(9)-(5)}{(8)-(4)} \\= \frac{9-5}{8-4} \\= \frac{4}{4} \\= 1[/tex]
Therefore, the slope is 1.
2) Any line that is in a "y = a number" format is a horizontal line, and all horizontal lines have a slope of 0 - so the second option can't be the answer.
The rest of the options are in slope-intercept form, or y = mx + b format. Remember that the coefficient of the term with the x is the slope. Knowing this, y = x + 1 would need to be the answer since the coefficient of the term with the x is 1, and we already calculated that the slope is 1.
