Question

Question 27 (1 point)(01.05)What is the slope-intercept form equation of the line that passes through (5, 7) and (8, 22)? (1 point)Oay = -5x + 18Oby = 5x - 18cy = -5x - 18Ody = 5x + 18

Answer 1

The slope-intercept form of a line is expressed as follows;

`y=mx+b`

Where;

`\begin{gathered} m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

To begin, we shall calculate the slope as shown below;

`m=(y_2-y_1)/(x_2-x_1)`

Using the two points given, we have;

`\begin{gathered} (x_1,y_1)\Rightarrow(5,7) \\ (x_2,y_2)\Rightarrow(8,22) \end{gathered}`

Therefore;

`\begin{gathered} m=(y_2-y_1)/(x_2-x_1) \\ m=(22-7)/(8-5) \\ m=(15)/(3) \\ m=5 \end{gathered}`

To calculate the y-intercept, we shall insert the value of m into the equation, y = mx + b. We shall use the first point which is (5, 7).

Note that if we use the second point (that is 8, 22) the value of the y-intercept would be the same.

Hence we have;

`\begin{gathered} x=5, \\ y=7 \\ m=5 \\ y=mx+b\text{ now becomes;} \\ 7=5(5)+b \\ 7=25+b \end{gathered}`

Subtract 25 from both sides;

`\begin{gathered} -18=b \\ b=-18 \end{gathered}`

Now that we have the values of m and b, (the slope and the y-intercept), the equation becomes;

`\begin{gathered} y=mx+b \\ y=5x+(-18) \\ y=5x-18 \end{gathered}`

ANSWER:

The correct answer is option (b);

`y=5x-18`