Maths-
SAT
Easy
Question
Which of the following statements is true about the graph of the equation 2y − 3x = −4 in the xy-plane?
- It has a negative slope and a positive y-intercept.
- It has a negative slope and a negative y-intercept.
- It has a positive slope and a positive y-intercept.
- It has a positive slope and a negative y-intercept.
The correct answer is: It has a positive slope and a negative y-intercept.
○ The concept used in this question is the concept of lines.
○ Equation of line is given by y = mx + c
Where y is y-coordinate, x is x-coordinate and c is the y-intercept (the point at which the line crosses the y -axis).
○ The slope of the line is the angle it makes with the x-axis i.e θ
○ The slope of line m is tan θ.
- Step by step explanation:
○ Given:
The equation given is equation of line in xy plane.
○ Step 1:
We know that the general equation of line lies in xy plane is given by,
y = mx + c ,
where m is the slope of the line or gradient.
○ Step 2:
○ Rearrange the given equation in form of y = mx + c
2y − 3x = −4
2y = 3x - 4
y = 
y = 
○ Step 3:
○ Compare above equation with y = mx + c
We will get,
m = 
and c = -2
∴ equation has positive slope i.e and
negative y-intercept i.e - 2
Correct option is,
Option D. It has a positive slope and a negative y-intercept.
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