Question

What is the y intercept for a line with point (-3, 1) slope -2?

Answer 1

Hint: This type of question depends on the equation of line passing through the given point and having slope m. In such question first we find the equation of the line by using the format \[(y-{{y}_{1}})=m(x-{{x}_{1}})\] where m is the given slope and \[({{x}_{1}},{{y}_{1}})\] are the coordinates of the given point. After finding the equation of line we compare it with the slope-intercept form \[y=mx+c\] to obtain c that is the y-intercept of the line.

Complete step by step solution:
We have to find the y intercept for a line with point (-3, 1) slope -2.
Consider, Format of the equation with slope and coordinates of one point \[(y-{{y}_{1}})=m(x-{{x}_{1}})\]
From the given data we can write,
\[\Rightarrow {{x}_{1}}=-3,{{y}_{1}}=1\And m=-2\]
Hence, the above equation becomes,
\[\Rightarrow (y-1)=(-2)\times [x-(-3)]\]
\[\begin{align}
  & \Rightarrow (y-1)=(-2)\times \left( x+3 \right) \\
 & \Rightarrow \left( y-1 \right)=-2x-6 \\
 & \Rightarrow y=-2x-6+1 \\
 & \Rightarrow y=-2x-5 \\
\end{align}\]
Hence, the equation of the line with point (-3, 1) and slope -2 is \[y=-2x-5\]
Now, comparing the equation of the line with point (-3, 1) and slope -2 that is \[y=-2x-5\] with slope-intercept form that is \[y=mx+c\] we get,
\[\Rightarrow m=-2\And c=-5\]
But $m$ represents the slope of the line and $c$ represents y-intercept of the line.
Hence, the y-intercept of the equation of the line with point (-3, 1) and slope -2 is -5.

Note: While solving this problem when students use basic rules of addition, subtraction and multiplication they have to take care about the change in sign when a number is shifted from left to right or right to left sides. It is important that students recollect and use the equation \[(y-{{y}_{1}})=m(x-{{x}_{1}})\] properly and then move on to the equation of the form \[y=mx+c\].