Question

An equation has a slope of 22.4 and passes through the point ,(0.4, 25.3), what is the line equation of the line when written in point slope form and slope-intercept form?

Answer 1

When we write a line equation, it can be written in point-slope form. This form is

`(y-y_1)=m(x-x_1)`

Where m represents the slope of the line, and (x1, y1) are the coordinates of a given point of the line.

Since we already have the slope and point, we can just substitute them on this form.

The line equation written in point-slope form is

`(y-25.3)=22.4(x-0.4)`

The slope-intercept form is

`y=mx+b`

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

Since we already have the equation in point-slope form, we can just rewrite the equation

`\begin{gathered} (y-25.3)=22.4(x-0.4) \\ y=22.4(x-0.4)+25.3 \\ y=22.4x-8.96+25.3 \\ y=22.4x+16.34 \end{gathered}`

And this is our equation in slope-intercept form

`y=22.4x+16.34`