How do you write an equation in slope-intercept form of the line that passes through the points (-2, 6.9) and (-4, 4.6)?

2 Answers
Apr 13, 2018

y=1.15x+9.2 is the slope - intercept form

Slope=m=1.15,y-intercept =9.2

Explanation:

Equation of a line, knowing two points on it is given by

yy1y2y1=xx1x2x1

(x1,y1)=2,6.9),(x2,y2)=(4,4.6)

y6.94.66.9=x+24+2

y6.92.3=x+22

(y6.9)=2.3(x+2)2, cross multiplying

y=1.15(x+2)+6.9

y=1.15x+9.2 is the slope - intercept form

Slope=m=1.15,y-intercept =9.2

Apr 13, 2018

y=1.15x+9.2

Explanation:

Since this is a linear variation of the form y=mx+b, any change in x will create a proportional change in y.
(2)(4)=2 and
(6.9)(4.6)=2.3 so
for every 2 changes in x, y changes by 2.3.
Divide each side by 2, and 1 change in x corresponds to 1.15 in y, therefore the slope (m) must be 1.15.
Now we have the equation y=1.15x+b
Before, we said our change in x by 2 resulted in a change in y of 2.3. Therefore, if we move over right 2 from (2,6.9), we reach the point (0,9.2). Since the x-value is 0, this is the y-intercept (b)
The equation is y=1.15x+9.2