Question

How do you write an equation with X-intercept of -3 and Y-intercept of 2?

Answer 1

Hint: This question belongs to the topic of straight line. For solving this question, we are going to use some formulas for this topic. In this question, first we will find the slope of line using the intercepts. After that, we will find the equation of line using the value of slope and one of the intercepts. We will find the equation of the line using the point-slope form of a line.

Complete step-by-step answer:
Let us solve this question.
The question is asking us to find the equation of line in which the equation has x-intercept of -3 and y-intercept of 2. That means the equation of the line which we have to find is intersecting the x-axis at -3 and also intersecting y-axis at 2.
As we know that the line is intersecting x-axis at -3. So, we can say that the line whose equation we have to find is having a point on the x-axis. The point is (-3,0).
Similarly, we know that the line is intersecting the y-axis at 2. So, we can say that line is having a point on the y-axis. The point on the y-axis is (0,2).
As we know that the formula of slope for a straight line is
\[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\], where m is the slope of straight line and \[\left( {{x}_{1}},{{y}_{1}} \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)\] are the points on the straight line.
Now, we can say that the line whose equation we have to find is having the points \[\left( -3,0 \right)\] and \[\left( 0,2 \right)\].
Here, we can say that \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( -3,0 \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)=\left( 0,2 \right)\].
So, now we can find the value of slope for the line.
\[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\dfrac{2-0}{0-\left( -3 \right)}=\dfrac{2}{3}\]
Hence, the value of slope is\[m=\dfrac{2}{3}\].
Now, we will use point-slope form to find the equation of line.
The general formula for point-slope form of a line is
\[y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)\], where m is the slope of line and \[\left( {{x}_{1}},{{y}_{1}} \right)\] is the point on the line.
So, here the value of slope is \[m=\dfrac{2}{3}\] and the point is \[\left( {{x}_{1}},{{y}_{1}} \right)=\left( -3,0 \right)\].
So, equation of line using point-slope form will be
\[y-0=\dfrac{2}{3}\left( x-\left( -3 \right) \right)\]
The above equation can also be written as
\[\Rightarrow y=\dfrac{2}{3}\left( x+3 \right)\]
On multiplying 3 to the both side of equation, we can write the above equation as
\[\Rightarrow 3y=2\left( x+3 \right)\]
We can write the above equation as
\[\Rightarrow 3y=2x+6\]
Hence, we get the equation of line as
\[3y=2x+6\]

Note: For solving this question, we should have better knowledge in the topic straight line. We should know the formula of slope for solving this type of question. And, also we should know the standard form, slope-intercept form, and point slope form for solving this type of question easily. The formula for slope is \[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\], here m is the slope and \[\left( {{x}_{1}},{{y}_{1}} \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)\] are the points of the straight line.
We have used point-slope form here.
All the forms of straight line are given below.
Standard form: \[Ax+By=C\]
Point-slope form: \[y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)\]
Slope-intercept form: \[y=mx+c\]