Question

Use slope-intercept form to write an equation of a line passing through the given point and having the given slope. Express the answer in standard form.P(−4, 1); m = 1

Answer 1

Recall that the slope-intercept form of the equation of a line is as follows:

$\begin{gathered} y=mx+b, \\ where\text{ m is the slope of the line and \lparen0,b\rparen is the y-intercept.} \end{gathered}$

Also, the standard form of the equation of a line is as follows:

$\begin{gathered} Ax+By=C, \\ Where\text{ A, B, and C are integers and A>0.} \end{gathered}$

Then the slope-intercept form of an equation with slope m=1 is as follows:

$y=x+b.$

Now, we know that the line passes through (-4,1), then:

$1=-4+b.$

Adding 4 to the above equation we get:

$\begin{gathered} 1+4=-4+b+4, \\ 5=b. \end{gathered}$

Therefore the slope-intercept form of the equation that passes through (-4,1) and has a slope of m=1 is:

$y=x+5.$

Adding -y-5 to the above equation we get:

$\begin{gathered} y-y-5=x+5-y-5, \\ -5=x-y. \end{gathered}$

Answer:

$x-y=-5.$