Explanation:
The equation for a line in the slope-intercept form is:
[tex]y=mx+b[/tex]
Where 'm' is the slope and 'b' is the y-intercept.
We can find both with only two points from the line. The slope is:
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_1-y_2}{x_1-x_2}[/tex]
(x1, y1) and (x2, y2) are points on the line.
With only one of these points, once we know the slope, we can find the y-intercept by replacing x and y by the point. For example:
[tex]y_1=mx_1+b[/tex]
And then solve for b.
In this problem we can use any pair of points from the table. I'll use the first two:
• (3, -4.5)
,
• (5, -9.5)
The slope is:
[tex]m=\frac{-4.5-(-9.5)}{3-5}=\frac{-4.5+9.5}{-2}=\frac{5}{-2}=-\frac{5}{2}[/tex]
And the y-intercept - I'll use point (3, -4.5) to find it;
[tex]\begin{gathered} -4.5=-\frac{5}{2}\cdot3+b \\ -4.5=-\frac{15}{2}+b \\ b=-4.5+\frac{15}{2}=-\frac{9}{2}+\frac{15}{2}=\frac{6}{2}=3 \end{gathered}[/tex]
Answer:
• Slope: -5/2
,
• y-intercept: 3
The correct answer is option B
