Question

A line passing through (4,2) and (5,4) in slope-intercept form

Answer 1

Given the points:

(x1, y1) ==> (4, 2)

(x2, y2) ==> (5, 4)

Let's find the line passing through the points in slope-intercept form.

Apply the slope-intercept form of a linear equation:

y = mx + b

Where m is the slope and b represents the y-intercept.

To find the slope, m, apply the formula:

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

Thus, we have:

`\begin{gathered} m=(4-2)/(5-4) \\ \\ m=(2)/(1) \\ \\ m=2 \end{gathered}`

The slope, m is 2.

We have:

`y=2x+b`

Plug in the values of one point for x and y to solve for b.

Take the first point:

(x, y) ==> (4, 2):

`\begin{gathered} 2=2(4)+b \\ \\ 2=8+b \\ \\ Subtract\text{ 8 from both sides:} \\ 2-8=8-8+b \\ \\ -6=b \\ \\ b=-6 \end{gathered}`

Therefore, the y-intercept, b, = -6.

The equation of the line passing through the points in slope-intercept form is:

`y=2x-6`

• ANSWER:

`y=2x-6`