Question

Tools Pencil Guideline Eliminator Sticky Notes Formulas Graphing Calculator Graph Paper Х y 5 Clear Mark 3 -4.5 5 -9.5 7 - 14.5 9 - 19.5 What are the slope and the y-intercept of the graph of this function? A Slope = 2, y-intercept = -4.5 5 B Slope = y-intercept = 3 2 © Slope = 2, y-intercept = -5 D Slope = 2 5 y-intercept = 3

Answer 1

Step-by-step explanation:

The equation for a line in the slope-intercept form is:

`y=mx+b`

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:

`m=(\Delta y)/(\Delta x)=(y_1-y_2)/(x_1-x_2)`

(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:

`y_1=mx_1+b`

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:

`m=(-4.5-(-9.5))/(3-5)=(-4.5+9.5)/(-2)=(5)/(-2)=-(5)/(2)`

And the y-intercept - I'll use point (3, -4.5) to find it;

`\begin{gathered} -4.5=-(5)/(2)\cdot3+b \\ -4.5=-(15)/(2)+b \\ b=-4.5+(15)/(2)=-(9)/(2)+(15)/(2)=(6)/(2)=3 \end{gathered}`

Answer:

• Slope: -5/2

,

• y-intercept: 3

The correct answer is option B