How do you write the equation in slope intercept form given (5, 1), (0, -6)?

1 Answer
Jim G.
Jul 24, 2016

#y=7/5x-6#

Explanation:

The equation of a line in #color(blue)"slope-intercept form"# is

#color(red)(|bar(ul(color(white)(a/a)color(black)(y=mx+b)color(white)(a/a)|)))#
where m represents the slope and b, the y-intercept.

To obtain the equation, we require to find m and b.

To calculate m, use the #color(blue)"gradient formula"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(a/a)|)))#
where # (x_1,y_1)" and " (x_2,y_2)" are 2 points"#

The 2 points here are (5 ,1) and (0 ,-6)

let # (x_1,y_1)=(5,1)" and " (x_2,y_2)=(0 ,-6)#

#rArrm=(-6-1)/(0-5)=(-7)/(-5)=7/5#

We are given the point (0 ,-6) which is the point where the line crosses the y-axis, hence the y-intercept b = -6

#rArry=7/5x-6" is the equation in slope-intercept form."#

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