Question

Find the slope, write a equation for the line, find values for a and b explain or show reasoning.

Answer 1

Given the graph of a line

For the given line, we will calculate the slope and find the equation of the line

As shown, the line passes through the points (2, 2) and (6, 10)

The slope of the line will be:

$slope=m=\frac{rise}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{10-2}{6-2}=\frac{8}{4}=2$

The slope-intercept form of the equation of the line is: y = m * x + b

Substitute with (m), the equation of the line will be:

$y=2x+b$

Substitute with (m) and the point (6, 10) to find the value of (b)

$\begin{gathered} 10=2\cdot6+b \\ 10=12+b \\ b=10-12=-2 \end{gathered}$

So, the answer will be:

Slope = m = 2

The equation of the line ⇒ y = 2x -2

Now, we will find the values of (a) and (b) shown in the figure:

The line passes with the point (a, 8)

So, we will find the value of (a) which make y = 8

So, substitute with (x=a) and (y=8) then solve for (a):

$\begin{gathered} 8=2a-2 \\ 8+2=2a \\ 10=2a \\ a=\frac{10}{2}=5 \end{gathered}$

And, the line passes with the point (4, b)

So, we will find the value of (b) which make x = 4

So, substitute with (x=4) and (y=b) then solve for (b):

$\begin{gathered} b=2\cdot4-2 \\ b=8-2 \\ b=6 \end{gathered}$

So,

$\begin{gathered} a=5 \\ b=6 \end{gathered}$