Answer:
y = 2x + 2
Step-by-step explanation:
Reading the graph!
- The line shown in the figure cuts the y-axis 2 units above the origin, I.e.,
the point (0, 2)
- The line also meets the x-axis two units before the origin, I.e.,
the point (-1, 0)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Intercepts:
When a line meets both the axes (x-axis and y-axis), it forms intercepts.
There are two types of intercepts:
- x-intercept (when the line meets the x-axis)
- y-intercept (when the line meets the y-axis)
Each of their length is equal to their distance from the Origin(0, 0)
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Equation of a line (intercept form):
If the x-intercept is denoted by "a" and y-intercept by "b", the equation if such a line is given by:
[tex] \boxed{ \mathsf{ \frac{x}{a} + \frac{y}{b} = 1 }}[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Equation of the line in question:
- x-intercept (a) = -1
- y-intercept (b) = 2
[tex] \implies \mathsf{ \frac{x}{( - 1)} + \frac{y}{2} = 1 }[/tex]
The sign of the denominator is taken by the numerator:
[tex]\implies \mathsf{ - \frac{x}{1} + \frac{y}{2} = 1 }[/tex]
Taking LCM:
[tex]\implies \mathsf{ \frac{ - 2x + y}{ 2} = 1 }[/tex]
Cross multiplying:
[tex]\implies \mathsf{ - 2x + y = 2 }[/tex]
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Isolating y:
[tex]\implies \mathsf{ \underline{ y = 2 + 2x }}[/tex]
That's the equation of the given line!
